A055807 -id:A055807 - cp's OEIS frontend

A055809 a(n) = T(n,n-4), array T as in A055807.

1, 15, 32, 56, 88, 129, 180, 242, 316, 403, 504, 620, 752, 901, 1068, 1254, 1460, 1687, 1936, 2208, 2504, 2825, 3172, 3546, 3948, 4379, 4840, 5332, 5856, 6413, 7004, 7630, 8292, 8991, 9728, 10504, 11320, 12177, 13076

Offset: 4

Clark Kimberling, May 28 2000

If Y_i (i=1,2,3,4) are 2-blocks of an n-set X then, for n>=8, a(n-2) is the number of (n-3)-subsets of X intersecting each Y_i (i=1,2,3,4). - Milan Janjic, Nov 09 2007

G. C. Greubel, Table of n, a(n) for n = 4..1000
Milan Janjic, Two Enumerative Functions
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A055807, A055810, A055811, A055815, A055816, A055817.

Concatenation([1], List([5..50], n-> n*(n^2 +3*n -22)/6 )); # G. C. Greubel, Jan 23 2020

[1] cat [n*(n^2 +3*n -22)/6: n in [5..50]]; // G. C. Greubel, Jan 23 2020

seq( `if`(n=4, 1, n*(n^2 +3*n -22)/6), n=4..50); # G. C. Greubel, Jan 23 2020

f[n_]:=Sum[i+i^2-8,{i,1,n}]/2;Table[f[n],{n,5,5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2010 *)
Table[If[n==4, 1, n*(n^2 +3*n -22)/6], {n,4,50}] (* G. C. Greubel, Jan 23 2020 *)

Vec(x^4*(1 + 11*x - 22*x^2 + 14*x^3 - 3*x^4)/(1-x)^4 + O(x^50)) \\ Michel Marcus, Jan 10 2015

vector(50, n, my(m=n+3); if(m==4, 1, m*(m^2 +3*m -22)/6)) \\ G. C. Greubel, Jan 23 2020

[1]+[n*(n^2 +3*n -22)/6 for n in (5..50)] # G. C. Greubel, Jan 23 2020

For n>4, a(n) = n*(n^2 + 3*n - 22)/6.
G.f.: x^4*(1 + 11*x - 22*x^2 + 14*x^3 - 3*x^4)/(1-x)^4. - Colin Barker, Feb 22 2012
E.g.f.: x*(72 +48*x +8*x^2 -3*x^2 + (-72 +24*x +4*x^2)*exp(x))/24. - G. C. Greubel, Jan 23 2020

A055810 a(n) = T(n,n-5), array T as in A055807.

Original entry on oeis.org

1, 31, 80, 160, 280, 450, 681, 985, 1375, 1865, 2470, 3206, 4090, 5140, 6375, 7815, 9481, 11395, 13580, 16060, 18860, 22006, 25525, 29445, 33795, 38605, 43906, 49730, 56110, 63080, 70675, 78931, 87885, 97575

Offset: 5

Clark Kimberling, May 28 2000

G. C. Greubel, Table of n, a(n) for n = 5..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A055807, A055809, A055811, A055815, A055816, A055817.

Concatenation([1], List([6..40], n-> (240 -54*n -49*n^2 +6*n^3 +n^4)/24 )); # G. C. Greubel, Jan 23 2020

[1] cat [(240 -54*n -49*n^2 +6*n^3 +n^4)/24: n in [6..40]]; // G. C. Greubel, Jan 23 2020

seq( `if`(n=5, 1, (240 -54*n -49*n^2 +6*n^3 +n^4)/24), n=5..40); # G. C. Greubel, Jan 23 2020

Table[If[n==5, 1, (240 -54*n -49*n^2 +6*n^3 +n^4)/24], {n,5,40}] (* G. C. Greubel, Jan 23 2020 *)

vector(40, n, my(m=n+4); if(m==5, 1, (240 -54*m -49*m^2 +6*m^3 +m^4)/24)) \\ G. C. Greubel, Jan 23 2020

[1]+[(240 -54*n -49*n^2 +6*n^3 +n^4)/24 for n in (6..40)] # G. C. Greubel, Jan 23 2020

G.f.: x^5*(1 +26*x -65*x^2 +60*x^3 -25*x^4 +4*x^5)/(1-x)^5. - Colin Barker, Feb 22 2012
From G. C. Greubel, Jan 23 2020: (Start)
a(n) = (240 -54*n -49*n^2 +6*n^3 +n^4)/24 for n > 5, with a(5) = 1.
E.g.f.: (-1200 -720*x +100*x^3 +25*x^4 -4*x^5 + (1200 -480*x -120*x^2 +60*x^3  +5*x^4)*exp(x))/120. (End)

A055811 a(n) = T(n,n-6), array T as in A055807.

Original entry on oeis.org

1, 63, 192, 432, 832, 1452, 2364, 3653, 5418, 7773, 10848, 14790, 19764, 25954, 33564, 42819, 53966, 67275, 83040, 101580, 123240, 148392, 177436, 210801, 248946, 292361, 341568, 397122, 459612, 529662

Offset: 6

Clark Kimberling, May 28 2000

G. C. Greubel, Table of n, a(n) for n = 6..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A055807, A055809, A055810, A055815, A055816, A055817.

Concatenation([1], List([7..30], n-> n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120 )); # G. C. Greubel, Jan 23 2020

[1] cat [n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120: n in [7.30]]; // G. C. Greubel, Jan 23 2020

seq( `if`(n=6, 1, n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120), n=6..30); # G. C. Greubel, Jan 23 2020

Table[If[n==6,1, n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120], {n,6,30}] (* G. C. Greubel, Jan 23 2020 *)

vector(25, n, my(m=n+5); if(m==6,1, m*(1584 -310*m -85*m^2 +10*m^3 +m^4)/120) ) \\ G. C. Greubel, Jan 23 2020

[1]+[n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120 for n in (7..30)] # G. C. Greubel, Jan 23 2020

From G. C. Greubel, Jan 23 2020: (Start)
a(n) = n*(1584 - 310*n - 85*n^2 + 10*n^3 + n^4)/120 for n > 6, with a(6) = 1.
G.f.: x^6*(1 + 57*x - 171*x^2 + 205*x^3 - 125*x^4 + 39*x^5 - 5*x^6)/(1-x)^6.
E.g.f.: (-1)*x*(7200 +4320*x +720*x^2 -120*x^3 -54*x^4 +5*x^5 - (7200 -2880*x + 120*x^3 + 6*x^4)*exp(x))/720. (End)

A055815 a(n) = T(2*n+3,n), array T as in A055807.

Original entry on oeis.org

1, 15, 80, 432, 2352, 12896, 71136, 394400, 2196128, 12273648, 68811184, 386838480, 2179890000, 12309739968, 69641542848, 394643939904, 2239678552640, 12727572969680, 72415319422992, 412470467298032

Offset: 0

Clark Kimberling, May 28 2000

nonn

G. C. Greubel, Table of n, a(n) for n = 0..250

Apart from the offset the same as A050149. - R. J. Mathar, Oct 13 2008

Cf. A055807, A055809, A055810, A055811, A055816, A055817.

T:= proc(i, j) option remember;
      if j=0 then 1
    elif i=0 then 0
    else add(add(T(h,m), m=0..j), h=0..i-1)
  fi; end:
seq(T(n+3, n), n=0..20); # G. C. Greubel, Jan 23 2020

T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]]; Table[T[n+3, n], {n,0,20}] (* G. C. Greubel, Jan 23 2020 *)

@CachedFunction
def T(i, j):
    if (j==0): return 1
    elif (i==0): return 0
    else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
[T(n+3, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020

a(n) = (n+3)*hypergeom([-n-2, n], [2], -1) = Sum_{s=1..n+3} binomial(n+3,s) * binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021

A055816 a(n) = T(2*n+4,n), array T as in A055807.

Original entry on oeis.org

1, 31, 192, 1120, 6400, 36288, 205184, 1159488, 6554880, 37088480, 210075712, 1191254688, 6762782208, 38434677120, 218663320320, 1245254943872, 7098135387648, 40495661150112, 231220652273600, 1321222104326880

Offset: 0

Clark Kimberling, May 28 2000

nonn

G. C. Greubel, Table of n, a(n) for n = 0..250

Cf. A055807, A055809, A055810, A055811, A055815, A055817.

T:= proc(i, j) option remember;
      if j=0 then 1
    elif i=0 then 0
    else add(add(T(h,m), m=0..j), h=0..i-1)
  fi; end:
seq(T(n+4, n), n=0..20); # G. C. Greubel, Jan 23 2020

T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]]; Table[T[n+4, n], {n,0,20}] (* G. C. Greubel, Jan 23 2020 *)

@CachedFunction
def T(i, j):
    if (j==0): return 1
    elif (i==0): return 0
    else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
[T(n+4, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020

a(n) = (n+4)*hypergeom([-n -3, n], [2], -1) = Sum_{s=1..n+4} binomial(n+4,s)*binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021

A055817 a(n) = T(2n+5,n), array T as in A055807.

Original entry on oeis.org

1, 63, 448, 2816, 16896, 99200, 575872, 3322112, 19096064, 109541824, 627653440, 3594256896, 20577979392, 117814911744, 674630384384, 3864033226240, 22138650598400, 126885674577728, 727501822004416, 4172725286118656

Offset: 0

Clark Kimberling, May 28 2000

nonn

G. C. Greubel, Table of n, a(n) for n = 0..250

Cf. A055807, A055809, A055810, A055811, A055815, A055816.

T:= proc(i, j) option remember;
      if j=0 then 1
    elif i=0 then 0
    else add(add(T(h,m), m=0..j), h=0..i-1)
  fi; end:
seq(T(n+5, n), n=0..20); # G. C. Greubel, Jan 23 2020

T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]]; Table[T[n+5, n], {n,0,20}] (* G. C. Greubel, Jan 23 2020 *)

@CachedFunction
def T(i, j):
    if (j==0): return 1
    elif (i==0): return 0
    else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
[T(n+5, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020

a(n) = (n+5)*hypergeom([-n-4, n], [2], -1) = Sum_{s=1..n+5} binomial(n+5,s) * binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021

A050147 a(n) = T(n,n-1), array T as in A050143. Also T(2n+1,n), array T as in A055807.

Original entry on oeis.org

1, 3, 12, 56, 280, 1452, 7700, 41456, 225648, 1238420, 6840988, 37986984, 211842696, 1185635388, 6655993380, 37463920608, 211350457824, 1194706644516, 6765300359468, 38370431711000, 217931108199672

Offset: 1

Clark Kimberling

nonn

Cf. A002003, A006318, A050143, A055807.

a[n_]:=Binomial[2*n-3,n-1]*Hypergeometric2F1[-n+1,-n,-2*n+3,-1];
Table[a[n],{n,1,21}] (* Detlef Meya, Dec 04 2023 *)

a(n):=if n=1 then 1 else sum((binomial(n,i+1))*binomial(n+i-2,n-2),i,0,n-2)+binomial(2*n-3,n-2); /* Vladimir Kruchinin, Nov 25 2014 */

From Vladimir Kruchinin, Nov 25 2014: (Start)
G.f.: x*((-x^2 + 4*x + 1)/(2*sqrt(x^2 - 6*x + 1)) -x/2 + 1/2).
For n >= 2, a(n) = C(2*n-3,n-2) + Sum_{i=0..n-2} C(n,i+1)*C(n+i-2,n-2). (End)
a(n) ~ (1 + sqrt(2))^(2*n-2) / (2^(1/4) * sqrt(Pi*n)). - Vaclav Kotesovec, Feb 14 2021
a(n) = binomial(2*n-3, n-1)*hypergeom([-n+1, -n], [-2*n+3], -1). - Detlef Meya, Dec 04 2023
D-finite with recurrence (-n+1)*a(n) +(2*n+3)*a(n-1) +3*(8*n-29)*a(n-2) +(-10*n+49)*a(n-3) +(n-6)*a(n-4)=0. - R. J. Mathar, Jul 31 2025

A050143 A(n,k) = Sum_{h=0..n-1, m=0..k} A(h,m) for n >= 1 and k >= 1, with A(n,0) = 1 for n >= 0 and A(0,k) = 0 for k >= 1; square array A, read by descending antidiagonals.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 4, 7, 1, 0, 1, 5, 12, 15, 1, 0, 1, 6, 18, 32, 31, 1, 0, 1, 7, 25, 56, 80, 63, 1, 0, 1, 8, 33, 88, 160, 192, 127, 1, 0, 1, 9, 42, 129, 280, 432, 448, 255, 1, 0, 1, 10, 52, 180, 450, 832, 1120, 1024, 511, 1

Offset: 1

Clark Kimberling

The triangular version of this square array is defined by T(n,k) = A(k,n-k) for 0 <= k <= n. Conversely, A(n,k) = T(n+k,n) for n,k >= 0. We have [o.g.f of T](x,y) = [o.g.f. of A](x*y, x) and [o.g.f. of A](x,y) = [o.g.f. of T](y,x/y). - Petros Hadjicostas, Feb 11 2021
Formatted as a triangular array with offset (0,8), it is [0, 1, 0, -1, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 1, 0, 0, 0, 0, ...], where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 05 2006
The sum of the first two columns [of the rectangular array] gives the powers of 2; that is, Sum_{j=0..1} A(i,j) = 2^i, i >= 0. On the other hand, for i >= 1 and j >= 2, A(i,j) is the number of lattice paths of i-1 upsteps (1,1) and j-1 downsteps (1,-1) in which each downstep-free vertex is colored red or blue. A downstep-free vertex is one not incident with a downstep. For example, dots indicate the downstep-free vertices in the path .U.U.UDU.UDDU., and with i = j = 2, A(2,2) = 4 counts UD, *UD, DU, DU*, where asterisks indicate the red vertices. - David Callan, Aug 27 2011

			Square array A(n,k) (with rows n >= 0 and columns k >= 0) begins:
  1,   0,   0,    0,    0,    0,    0,     0,     0,     0, ...
  1,   1,   1,    1,    1,    1,    1,     1,     1,     1, ...
  1,   3,   4,    5,    6,    7,    8,     9,    10,    11, ...
  1,   7,  12,   18,   25,   33,   42,    52,    63,    75, ...
  1,  15,  32,   56,   88,  129,  180,   242,   316,   403, ...
  1,  31,  80,  160,  280,  450,  681,   985,  1375,  1865, ...
  1,  63, 192,  432,  832, 1452, 2364,  3653,  5418,  7773, ...
  1, 127, 448, 1120, 2352, 4424, 7700, 12642, 19825, 29953, ...
  ...
If we read the above square array by descending antidiagonals, we get the following triangular array T(n,k) (with rows n >= 0 and columns 0 <= k <= n):
   1;
   0, 1;
   0, 1, 1;
   0, 1, 3,  1;
   0, 1, 4,  7,   1;
   0, 1, 5, 12,  15,   1;
   0, 1, 6, 18,  32,  31,   1;
   0, 1, 7, 25,  56,  80,  63,   1;
   0, 1, 8, 33,  88, 160, 192, 127,   1;
   0, 1, 9, 42, 129, 280, 432, 448, 255, 1;
   ...

Yumin Cho, Jaehyun Kim, Jang Soo Kim, and Nakyung Lee, Enumeration of multiplex juggling card sequences using generalized q-derivatives, arXiv:2402.09903 [math.CO], 2024. See p. 9.
Clark Kimberling, Path-counting and Fibonacci numbers, Fib. Quart. 40(4) (2002), 328-338; see Example 3A and Eq. (8) on p. 333.

Antidiagonal sums are odd-indexed Fibonacci numbers (A001519).
Signed alternating antidiagonal sums are Fibonacci(n)-2, as in A001911.
Cf. A000225, A001792, A050147, A050148, A055807 (mirror array of triangle), A084938.

T[n_, k_] := If[n == k, 1, JacobiP[k - 1, 1, n - 2*k - 1, 3]];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Peter Luschny, Nov 25 2021 *)

Formulas for the square array (A(n,k): n,k >= 0):
A(n,1) = -1 + 2^n = A000225(n) for n >= 1.
A(n+2,2) = 4*A001792(n) for n >= 0.
From Petros Hadjicostas, Feb 11 2021: (Start)
Recurrence: A(n,k) = 2*A(n-1,k) + A(n,k-1) - A(n-1,k-1) for n >= 1 and k >= 2; with A(n,0) = 1 for n >= 0, A(0,k) = 0 for k >= 1, and A(n,1) = -1 + 2^n for n >= 1.
Bivariate o.g.f.: Sum_{n,k>=0} A(n,k)*x^n*y^k = (1 - 2*x)*(1 - y)/((1 - x)*(1 - 2*x - y + x*y)).
A(n,k) = Sum_{s=1..n} binomial(n,s)*binomial(s+k-2,k-1) for n >= 0 and k >= 1. (It can be proved by using a partial fraction decomposition on the bivariate o.g.f. above.)
A(n,k) = n*hypergeom([-n + 1, k], [2], -1) for n >= 0 and k >= 1. (End)
Formulas for the triangular array (T(n,k): 0 <= k <= n):
Sum_{k=0..n} T(n,k) = Fibonacci(2*n-1) = A001519(n) with Fibonacci(-1) = 1.
Sum_{k=0..n} (-1)^(n+k-1)*T(n,k) = Fibonacci(n+1) - 2 = A001911(n-2) with A001911(-2) = A001911(-1) = -1.
T(n,k) = A055807(n,n-k) for 0 <= k <= n.
From Petros Hadjicostas, Feb 12 2021: (Start)
Recurrence: T(n,k) = 2*T(n-1,k-1) + T(n-1,k) - T(n-2,k-1) for n >= 3 and 1 <= k <= n-2; with T(n,n) = 1 for n >= 0, T(n,0) = 0 for n >= 1, and T(n+1, n) = 2^n - 1 for n >= 1.
Bivariate o.g.f: Sum_{n,k>=0} T(n,k)*x^n*y^k = (1 - x)*(1 - 2*x*y)/((1 - x*y)*(1 - x - 2*x*y + x^2*y)).
T(n,k) = Sum_{s=1..k} binomial(k,s)*binomial(s+n-k-2, s-1) = k*hypergeom([-k+1, n-k], [2], -1) for n >= 1 and 0 <= k <= n - 1. (End)
T(n, k) = JacobiP(k - 1, 1, n - 2*k - 1, 3) n >= 0 and 0 <= k < n. - Peter Luschny, Nov 25 2021

Various sections edited by Petros Hadjicostas, Feb 12 2021

A050148 a(n) = T(n,n-2), array T as in A050143.

Original entry on oeis.org

1, 7, 32, 160, 832, 4424, 23872, 130176, 715520, 3957448, 21998176, 122786976, 687736896, 3863423880, 21758302848, 122811081216, 694533774336, 3934558067336, 22323615621280, 126832567223712, 721500116473664

Offset: 2

Clark Kimberling

nonn

Also T(2*n-2,n-2), array T as in A055807.

Cf. A050143, A055807.

a(n) = Sum_{s=1..n} binomial(n,s)*binomial(s+n-4,n-3) = n*hypergeom([-n + 1, n-2], [2], -1) for n >= 3. - Petros Hadjicostas, Feb 13 2021

D-finite with recurrence (n-1)*(n-3)*a(n) +(-8*n^2+41*n-48)*a(n-1) +(13*n^2-95*n+162)*a(n-2) -2*(n-2)*(n-6)*a(n-3)=0 for n-3>=3. - R. J. Mathar, Jul 31 2025

A111516 Triangle G(n,k) read by rows: number of order-preserving partial transformations (of an n-element totally ordered set) of waist k (waist(alpha) = max(Im(alpha))).

Original entry on oeis.org

1, 1, 1, 1, 3, 4, 1, 7, 12, 18, 1, 15, 32, 56, 88, 1, 31, 80, 160, 280, 450, 1, 63, 192, 432, 832, 1452, 2364, 1, 127, 448, 1120, 2352, 4424, 7700, 12642, 1, 255, 1024, 2816, 6400, 12896, 23872, 41456, 68464, 1, 511, 2304, 6912, 16896, 36288, 71136, 130176, 225648, 374274

Offset: 0

Abdullahi Umar, Aug 25 2008

			Triangle G(n,k) (with rows n >= 0 and columns k = 0..n) begins:
  1;
  1,  1;
  1,  3,   4;
  1,  7,  12,  18;
  1, 15,  32,  56,  88;
  1, 31,  80, 160, 280,  450;
  1, 63, 192, 432, 832, 1452, 2364;
  ...
G(2,2) = 4 because there are exactly 4 order-preserving partial transformations (on a 2-element chain) of waist 2, namely: (1)->(2), (2)->(2), (1,2)->(1,2), and (1,2)->(2,2) - the mappings are coordinate-wise.

A. Laradji and A. Umar, Combinatorial results for semigroups of order-preserving partial transformations, Journal of Algebra, 278, (2004), 342-359.
A. Laradji and A. Umar, Combinatorial results for semigroups of order-decreasing partial transformations, J. Integer Seq., 7 (2004), 04.3.8.

Cf. A050146 (main diagonal), A055807, A123164 (row sums).

G(n,k) = Sum_{j=1..n} C(n,j)*C(k+j-2,j-1) for 1 <= k <= n. [Corrected by Petros Hadjicostas, Feb 13 2021]
G(n,k) = 2*G(n-1,k) - G(n-1,k-1) + G(n,k-1) for n >= 2 and 1 <= k <= n-1 with initial conditions G(n,0) = 1 for n >= 0, G(n,1) = 2^n - 1 for n >= 1, and G(n,n) = A050146(n) for n >= 2.
Sum_{k=0..n} G(n,k) = A123164(n).
From Petros Hadjicostas, Feb 13 2021: (Start)
G(n,k) = A055807(n+k,k) for 0 <= k <= n.
Bivariate o.g.f.: Sum_{n,k>=0} G(n,k)*x^n*y^k = ((2 - 2*y - 2*x*y + x*y^2) + 2*x*(y - 1)/(1 - x) + x*y*(2 - 3*y - 2*x*y + x*y^2)/sqrt(1 - 6*x*y + x^2*y^2))/(2*(1 - 2*x - y + x*y)). (End)

G(7,5) corrected by and more terms from Petros Hadjicostas, Feb 13 2021

cp's OEIS Frontend

A055809 a(n) = T(n,n-4), array T as in A055807.

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A055810 a(n) = T(n,n-5), array T as in A055807.

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A055811 a(n) = T(n,n-6), array T as in A055807.

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A055815 a(n) = T(2*n+3,n), array T as in A055807.

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A055816 a(n) = T(2*n+4,n), array T as in A055807.

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A055817 a(n) = T(2n+5,n), array T as in A055807.

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A050147 a(n) = T(n,n-1), array T as in A050143. Also T(2n+1,n), array T as in A055807.

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