A007701 -id:A007701 - cp's OEIS frontend

A023531 a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.

1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Clark Kimberling, Jun 14 1998

Can be read as table: a(n,m) = 1 if n = m >= 0, else 0 (unit matrix).
a(n) = number of 1's between successive 0's (see also A005614, A003589 and A007538). - Eric Angelini, Jul 06 2005
Triangle T(n,k), 0 <= k <= n, read by rows, given by A000004 DELTA A000007 where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 03 2009
Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order.
A023531 is reverse reluctant sequence of sequence A000007. - Boris Putievskiy, Jan 11 2013
Also the Bell transform (and the inverse Bell transform) of 0^n (A000007). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 19 2016
This is the turn sequence of the triangle spiral.  To form the spiral: go a unit step forward, turn left a(n)*120 degrees, and repeat.  The triangle sides are the runs of a(n)=0 (no turn).  The sequence can be generated by a morphism with a special symbol S for the start of the sequence: S -> S,1; 1 -> 0,1; 0->0.  The expansion lengthens each existing side and inserts a new unit side at the start.  See the Fractint L-system in the links to draw the spiral this way. - Kevin Ryde, Dec 06 2019

			As a triangle:
       1
      0 1
     0 0 1
    0 0 0 1
   0 0 0 0 1
  0 0 0 0 0 1
G.f. = 1 + x^2 + x^5 + x^9 + x^14 + x^20 + x^27 + x^35 + x^44 + x^54 + ...
From _Kevin Ryde_, Dec 06 2019: (Start)
.
              1            Triangular spiral: start at S;
             / \             go a unit step forward,
            0   0   .        turn left a(n)*120 degrees,
           /     \   .       repeat.
          0   1   0   .
         /   / \   \   \   Each side's length is 1 greater
        0   0   0   0   0    than that of the previous side.
       /   /     \   \   \
      0   0   S---1   0   0
     /   /             \   \
    0   1---0---0---0---1   0
   /                         \
  1---0---0---0---0---0---0---1
(End)

Antti Karttunen, Table of n, a(n) for n = 0..100127
Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), Article 00.2.4.
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.
Franck Ramaharo, A generating polynomial for the pretzel knot, arXiv:1805.10680 [math.CO], 2018.
Kevin Ryde, Fractint L-System drawing the spiral.
Eric Weisstein's World of Mathematics, Jacobi Theta Functions.
Eric Weisstein's World of Mathematics, Modified Bessel Function of the First Kind.
Index entries for characteristic functions.

Cf. A000217, A003057, A010054, A000007, A023532.

Cf. A000096, A007701, A024316.

a023531 n = a023531_list !! n
a023531_list = concat $ iterate ([0,1] *) [1]
instance Num a => Num [a] where
   fromInteger k = [fromInteger k]
   (p:ps) + (q:qs) = p + q : ps + qs
   ps + qs         = ps ++ qs
   (p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs
    *                = []
-- Reinhard Zumkeller, Apr 02 2011

seq(op([0$m,1]),m=0..10); # Robert Israel, Jan 18 2015
# alternative
A023531 := proc(n)
    option remember ;
    local m,t ;
    for m from 0 do
        t := m*(m+3)/2 ;
        if t > n then
            return 0 ;
        elif t = n then
            return 1 ;
        end if;
    end do:
end proc:
seq(A023531(n),n=0..40) ; # R. J. Mathar, May 15 2025

If[IntegerQ[(Sqrt[9+8#]-3)/2],1,0]&/@Range[0,100] (* Harvey P. Dale, Jul 27 2011 *)
a[ n_] := If[ n < 0, 0, Boole @ IntegerQ @ Sqrt[ 8 n + 9]]; (* Michael Somos, May 17 2014 *)
a[ n_] := SeriesCoefficient[ (EllipticTheta[ 2, 0, x^(1/2)] / (2 x^(1/8)) - 1) / x, {x, 0, n}]; (* Michael Somos, May 17 2014 *)

{a(n) = if( n<0, 0, issquare(8*n + 9))}; /* Michael Somos, May 17 2014 */

A023531(n)=issquare(8*n+9) \\ M. F. Hasler, Apr 12 2018

from math import isqrt
def A023531(n): return int((k:=n+1<<1)==(m:=isqrt(k))*(m+1)) # Chai Wah Wu, Nov 09 2024

def A023531_row(n) :
    if n == 0: return [1]
    return [0] + A023531_row(n-1)
for n in (0..9): print(A023531_row(n))  # Peter Luschny, Jul 22 2012

If (floor(sqrt(2*n))-(2*n/(floor(sqrt(2*n)))) = -1, 1, 0). - Gerald Hillier, Sep 11 2005
a(n) = 1 - A023532(n); a(n) = 1 - mod(floor(((10^(n+2) - 10)/9)10^(n+1 - binomial(floor((1+sqrt(9+8n))/2), 2) - (1+floor(log((10^(n+2) - 10)/9, 10))))), 10). - Paul Barry, May 25 2004
a(n) = floor((sqrt(9+8n)-1)/2) - floor((sqrt(1+8n)-1)/2). - Paul Barry, May 25 2004
a(n) = round(sqrt(2n+3)) - round(sqrt(2n+2)). - Hieronymus Fischer, Aug 06 2007
a(n) = ceiling(2*sqrt(2n+3)) - floor(2*sqrt(2n+2)) - 1. - Hieronymus Fischer, Aug 06 2007
From Franklin T. Adams-Watters, Jun 29 2009: (Start)
G.f.: (1/2 x^{-1/8}theta_2(0,x^{1/2}) - 1)/x, where theta_2 is a Jacobi theta function.
G.f. for triangle: Sum T(n,k) x^n y^k = 1/(1-x*y). Sum T(n,k) x^n y^k / n! = Sum T(n,k) x^n y^k / k! = exp(x*y). Sum T(n,k) x^n y^k / (n! k!) = I_0(2*sqrt(x*y)), where I is the modified Bessel function of the first kind. (End)
a(n) = A000007(m), where m=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Jan 11 2013
The row polynomials are p(n,x) = x^n = (-1)^n n!Lag(n,-n,x), the normalized, associated Laguerre polynomials of order -n. As the prototypical Appell sequence with e.g.f. exp(x*y), its raising operator is R = x and lowering operator, L = d/dx, i.e., R p(n,x) = p(n+1,x), and L p(n,x) = n * p(n-1,x). - Tom Copeland, May 10 2014
a(n) = A010054(n+1) if n >= 0. - Michael Somos, May 17 2014
a(n) = floor(sqrt(2*(n+1)+1/2)-1/2) - floor(sqrt(2*n+1/2)-1/2). - Mikael Aaltonen, Jan 18 2015
a(n) = A003057(n+3) - A003057(n+2). - Robert Israel, Jan 18 2015
a(A000096(n)) = 1; a(A007701(n)) = 0. - Reinhard Zumkeller, Feb 14 2015
Characteristic function of A000096. - M. F. Hasler, Apr 12 2018
Sum_{k=1..n} a(k) ~ sqrt(2*n). - Amiram Eldar, Jan 13 2024

A127670 Discriminants of Chebyshev S-polynomials A049310.

Original entry on oeis.org

1, 4, 32, 400, 6912, 153664, 4194304, 136048896, 5120000000, 219503494144, 10567230160896, 564668382613504, 33174037869887488, 2125764000000000000, 147573952589676412928, 11034809241396899282944, 884295678882933431599104, 75613185918270483380568064

Offset: 1

Wolfdieter Lang, Jan 23 2007

a(n-1) is the number of fixed n-cell polycubes that are proper in n-1 dimensions (Barequet et al., 2010).
From Rigoberto Florez, Sep 02 2018: (Start)
a(n-1) is the discriminant of the Morgan-Voyce Fibonacci-type polynomial B(n).
Morgan-Voyce Fibonacci-type polynomials are defined as B(0) = 0, B(1) = 1 and B(n) = (x+2)*B(n-1) - B(n-2) for n > 1.
The absolute value of the discriminant of Fibonacci polynomial F(n) is a(n-1).
Fibonacci polynomials are defined as F(0) = 0, F(1) = 1 and F(n) = x*F(n-1) + F(n-2) for n > 1. (End)
The first 6 values are the dimensions of the polynomial ring in 3n variables xi, yi, zi for 1 <= i <= n modulo the ideal generated by x1^a y1^b z1^c + ... + xn^a yn^b zn^c for 0 < a+b+c <= n (see Fact 2.8.1 in Haiman's paper). - Mike Zabrocki, Dec 31 2019

			n=3: The zeros are [sqrt(2),0,-sqrt(2)]. The Vn(xn[1],...,xn[n]) matrix is [[1,1,1],[sqrt(2),0,-sqrt(2)],[2,0,2]]. The squared determinant is 32 = a(3). - _Wolfdieter Lang_, Aug 07 2011

Gill Barequet, Solomon W. Golomb, and David A. Klarner, Polyominoes. (This is a revision, by G. Barequet, of the chapter of the same title originally written by the late D. A. Klarner for the first edition, and revised by the late S. W. Golomb for the second edition.) Preprint, 2016, http://www.csun.edu/~ctoth/Handbook/chap14.pdf.
G. Barequet and M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, 31st International Symposium on Computational Geometry (SoCG'15). Editors: Lars Arge and János Pach; pp. 19-22, 2015.
Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990; p. 219 for T and U polynomials.

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Andrei Asinowski, Gill Barequet, Ronnie Barequet, and Gunter Rote, Proper n-Cell Polycubes in n - 3 Dimensions, Journal of Integer Sequences, Vol. 15 (2012), #12.8.4.
Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012. See Th. 1. [From _N. J. A. Sloane_, Oct 16 2010]
R. Barequet, G. Barequet, and G. Rote, Formulae and growth rates of high-dimensional polycubes, Combinatorica 30 (2010), pp. 257-275.
Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.
Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
Rigoberto Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.
M. Haiman, Conjectures on the quotient ring by diagonal invariants, preprint, 1993.
M. Haiman, Conjectures on the quotient ring by diagonal invariants, J. Algebraic Combin. 3 (1994), no. 1, 17--76.
O. Khorunzhiy, Enumeration of tree-type diagrams assembled from oriented chains of edges, arXiv:2207.00766 [math.CO], 2022.
Andrew Snowden, Measures for the colored circle, arXiv:2302.08699 [math.CO], 2023.
Eric Weisstein's World of Mathematics, Discriminant
Eric Weisstein's World of Mathematics, Morgan-Voyce Polynomials
Eric Weisstein's World of Mathematics, Fibonacci Polynomial

Cf. A007701 (T-polynomials), A086804 (U-polynomials), A171860 and A191092 (fixed n-cell polycubes proper in n-2 and n-3 dimensions, resp.).
Cf. A243953, A006645, A001629, A001871, A006645, A007701, A045618, A045925, A093967, A193678, A317404, A317405, A317408, A317451, A318184, A318197.
A317403 is essentially the same sequence.
Diagonal 1 of A195739.

[((n+1)^n/(n+1)^2)*2^n: n in [1..20]]; // Vincenzo Librandi, Jun 23 2014

Table[((n + 1)^n)/(n + 1)^2 2^n, {n, 1, 30}] (* Vincenzo Librandi, Jun 23 2014 *)

a(n) = ((n+1)^(n-2))*2^n, n >= 1.
a(n) = (Det(Vn(xn[1],...,xn[n])))^2 with the determinant of the Vandermonde matrix Vn with elements (Vn)i,j:= xn[i]^j, i=1..n, j=0..n-1 and xn[i]:=2*cos(Pi*i/(n+1)), i=1..n, are the zeros of S(n,x):=U(n,x/2).
a(n) = ((-1)^(n*(n-1)/2))*Product_{j=1..n} ((d/dx)S(n,x)|_{x=xn[j]}), n >= 1, with the zeros xn[j], j=1..n, given above.
a(n) = A007830(n-2)*A000079(n), n >= 2. - Omar E. Pol, Aug 27 2011
E.g.f.: -LambertW(-2*x)*(2+LambertW(-2*x))/(4*x). - Vaclav Kotesovec, Jun 22 2014

Slightly edited by Gill Barequet, May 24 2011

A318184 a(n) = 2^(n * (n - 1)/2) * 3^((n - 1) * (n - 2)) * n^(n - 3).

Original entry on oeis.org

1, 1, 72, 186624, 13604889600, 24679069470425088, 1036715783690392172494848, 962459606796748852884396910313472, 19112837387997044228759204010262201783812096, 7926475921550134182551017087135940323782552453120000000, 67406870957147550175650545441605700298239194363455522532832462241792

Offset: 1

Rigoberto Florez, Aug 20 2018

nonn

Discriminant of Fermat polynomials.

F(0)=0, F(1)=1 and F(n) = 3x F(n - 1) -2 F(n - 2) if n>1.

Muniru A Asiru, Table of n, a(n) for n = 1..39
Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
Eric Weisstein's World of Mathematics, Discriminant
Eric Weisstein's World of Mathematics, Fermat Polynomial

Cf. A193678, A007701, A007701, A193678, A303941.

seq(2^(n*(n-1)/2)*3^((n-1)*(n-2))*n^(n-3),n=1..12); # Muniru A Asiru, Dec 07 2018

F[0] = 0; F[1] = 1; F[n_] := F[n] = 3 x F[n - 1] - 2 F[n - 2];
a[n_] := Discriminant[F[n], x];
Array[a, 11] (* Jean-François Alcover, Dec 07 2018 *)

a(n) = 2^(n*(n-1)/2) * 3^((n-1)*(n-2)) * n^(n-3); \\ Michel Marcus, Dec 07 2018

A318197 a(n) = 2^((n - 1)(n + 2)/2)3^(n(n - 1))n^n.

Original entry on oeis.org

1, 144, 629856, 69657034752, 178523361331200000, 10072680467275913619308544, 12094526244510115670028303294529536, 301689370251168256106930569591201258430005248, 153543958878683931150976515367278080485732740052794998784, 1572290138917723454985999517360927544173903258140620787548160000000000

Offset: 1

Rigoberto Florez, Aug 20 2018

nonn

Discriminant of Fermat-Lucas polynomials.

Fermat-Lucas polynomials are defined as F(0) = 2, F(1) = 3*x and F(n) = 3*x*F(n - 1) - 2*F(n - 2) for n > 1.

Andrew Howroyd, Table of n, a(n) for n = 1..30
Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
R. Flórez, R. Higuita, and A. Mukherjee, The Star of David and Other Patterns in Hosoya Polynomial Triangles, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.
R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.
Eric Weisstein's World of Mathematics, Discriminant
Eric Weisstein's World of Mathematics, Fermat-Lucas polynomials

Cf. A137372, A193678, A007701, A007701, A193678.

[2^((n - 1)*(n + 2) div 2)*3^(n*(n - 1))*n^n: n in [1..10]]; // Vincenzo Librandi, Aug 25 2018

Array[2^((# - 1) (# + 2)/2)*3^(# (# - 1))*#^# &, 10] (* Michael De Vlieger, Aug 22 2018 *)

apply(poldisc, Vec((2-3*x*y)/(1-3*y*x+2*x^2) - 2 + O(x^12))) \\ Andrew Howroyd, Aug 20 2018

a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n; \\ Andrew Howroyd, Aug 20 2018

A086804 a(0)=0; for n > 0, a(n) = (n+1)^(n-2)*2^(n^2).

Original entry on oeis.org

0, 1, 16, 2048, 1638400, 7247757312, 164995463643136, 18446744073709551616, 9803356117276277820358656, 24178516392292583494123520000000, 271732164163901599116133024293512544256

Offset: 0

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003

Discriminant of Chebyshev polynomial U_n (x) of second kind.
Chebyshev second kind polynomials are defined by U(0)=0, U(1)=1 and U(n) = 2xU(n-1) - U(n-2) for n > 1.
The absolute value of the discriminant of Pell polynomials is a(n-1).
Pell polynomials are defined by P(0)=0, P(1)=1 and P(n) = 2x P(n-1) + P(n-2) if n > 1. - Rigoberto Florez, Sep 01 2018

Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990; p. 219, 5.1.2.

Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.
R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.
Eric Weisstein's World of Mathematics, Discriminant
Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the Second Kind
Eric Weisstein's World of Mathematics, Pell Polynomial
Index entries for sequences related to Chebyshev polynomials.

Cf. A007701, A127670 (discriminant for S-polynomials), A006645, A001629, A001871, A006645, A007701, A045618, A045925, A093967, A193678, A317404, A317405, A317408, A317451, A318184, A318197.

[0] cat [(n+1)^(n-2)*2^(n^2): n in [1..10]]; // G. C. Greubel, Nov 11 2018

Join[{0},Table[(n+1)^(n-2) 2^n^2,{n,10}]] (* Harvey P. Dale, May 01 2015 *)

PARI
```
a(n)=if(n<1,0,(n+1)^(n-2)*2^(n^2))
```

a(n)=if(n<1,0,n++; poldisc(poltchebi(n)'/n))

a(n) = ((n+1)^(n-2))*2^(n^2), n >= 1, a(0):=0.
a(n) = ((2^(2*(n-1)))*Det(Vn(xn[1],...,xn[n])))^2, n >= 1, with the determinant of the Vandermonde matrix Vn with elements (Vn)i,j:= xn[i]^j, i=1..n, j=0..n-1 and xn[i]:=cos(Pi*i/(n+1)), i=1..n, are the zeros of the Chebyshev U(n,x) polynomials.
a(n) = ((-1)^(n*(n-1)/2))*(2^(n*(n-2)))*Product_{i=1..n}((d/dx)U(n,x)|_{x=xn[i]}), n >= 1, with the zeros xn[i], i=1..n, given above.

Formula and more terms from Vladeta Jovovic, Aug 07 2003

A123276 Discriminant of the Chebyshev polynomial of first kind of degree 2^n.

Original entry on oeis.org

1, 8, 131072, 9444732965739290427392, 994646472819573284310764496293641680200912301594695434880927953786318994025066751066112

Offset: 0

Benoit Cloitre, Oct 10 2006

nonn

Next term is too large to include.

Amiram Eldar, Table of n, a(n) for n = 0..5

Cf. A007701.

a[n_] := 2^(4^n + (n+1) * 2^n - 3 * 2^n+1); Array[a, 5, 0] (* Amiram Eldar, May 08 2025 *)

PARI
```
a(n)=2^(4^n+(n+1)*2^n-3*2^n+1);
```

a(n) = poldisc(polchebyshev(2^n, 1)); \\ Michel Marcus, Mar 02 2023

a(n) = 2^(4^n+(n+1)*2^n-3*2^n+1).

A317403 a(n)=(-1)^((n-2)(n-1)/2)2^(n-1)*n^(n-3).

Original entry on oeis.org

1, 1, -4, -32, 400, 6912, -153664, -4194304, 136048896, 5120000000, -219503494144, -10567230160896, 564668382613504, 33174037869887488, -2125764000000000000, -147573952589676412928, 11034809241396899282944, 884295678882933431599104, -75613185918270483380568064

Offset: 1

Rigoberto Florez, Aug 26 2018

sign

Discriminant of Fibonacci polynomials.

Fibonacci polynomials are defined as F(0)=0, F(1)=1 and F(n)=x*F(n-1)+F(n-2) for n>1. Coefficients are given in triangle A168561 with offset 1.

Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, 2018.
R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.
R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.
Eric Weisstein's World of Mathematics, Discriminant
Eric Weisstein's World of Mathematics, Fibonacci Polynomial

Cf. A006645, A001629, A001871, A006645, A007701, A045618, A045925, A093967, A168561, A193678, A317404, A317405, A317408, A317451, A318184, A318197.

Essentially the same as A127670.

[(-1)^((n-2)*(n-1) div 2)*2^(n-1)*n^(n-3): n in [1..20]]; // Vincenzo Librandi, Aug 27 2018

Array[(-1)^((#-2)*(#-1)/2)*2^(#-1)*#^(#-3)&,20]

concat([1], [poldisc(p) | p<-Vec(x/(1-x^2-y*x) - x + O(x^20))]) \\ Andrew Howroyd, Aug 26 2018

A317450 a(n)=(-1)^((n-2)(n-1)/2)2^((n-1)^2)*n^(n-3).

Original entry on oeis.org

1, 1, -16, -2048, 1638400, 7247757312, -164995463643136, -18446744073709551616, 9803356117276277820358656, 24178516392292583494123520000000, -271732164163901599116133024293512544256, -13717048991958695477963985711266803110069141504, 3074347100178259797134292590832254504315406543889629184

Offset: 1

Rigoberto Florez, Aug 26 2018

sign

Discriminant of Pell polynomials.

Pell polynomials are defined as P(0)=0, P(1)=1 and P(n)=2xP(n-1)+P(n-2) for n>1.

Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, 2018.
R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.
R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.
Eric Weisstein's World of Mathematics, Discriminant
Eric Weisstein's World of Mathematics, Pell Polynomial

Cf. A006645, A001629, A001871, A006645, A007701, A045618, A045925, A093967, A193678, A317404, A317405, A317408, A317451, A318184, A318197.

Essentially the same as A086804.

Array[(-1)^((#-2)*(#-1)/2)* 2^((#-1)^2)*#^(#-3)&,15]

cp's OEIS Frontend

A023531 a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.

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A127670 Discriminants of Chebyshev S-polynomials A049310.

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A318184 a(n) = 2^(n * (n - 1)/2) * 3^((n - 1) * (n - 2)) * n^(n - 3).

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A318197 a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n.

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A086804 a(0)=0; for n > 0, a(n) = (n+1)^(n-2)*2^(n^2).

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A123276 Discriminant of the Chebyshev polynomial of first kind of degree 2^n.

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A318197 a(n) = 2^((n - 1)(n + 2)/2)3^(n(n - 1))n^n.

A317403 a(n)=(-1)^((n-2)(n-1)/2)2^(n-1)*n^(n-3).

A317450 a(n)=(-1)^((n-2)(n-1)/2)2^((n-1)^2)*n^(n-3).