A062971 -id:A062971 - cp's OEIS frontend

A374848 Obverse convolution A000045**A000045; see Comments.

0, 1, 2, 16, 162, 3600, 147456, 12320100, 2058386904, 701841817600, 488286500625000, 696425232679321600, 2038348954317776486400, 12259459134020160144810000, 151596002479762016373851690400, 3855806813438155578522841251840000

Offset: 0

Clark Kimberling, Jul 31 2024

nonn

The obverse convolution of sequences
  s = (s(0), s(1), ...) and t = (t(0), t(1), ...)
is introduced here as the sequence s**t given by
s**t(n) = (s(0)+t(n)) * (s(1)+t(n-1)) * ... * (s(n)+t(0)).
Swapping * and + in the representation s(0)*t(n) + s(1)*t(n-1) + ... + s(n)*t(0)
of ordinary convolution yields s**t.
If x is an indeterminate or real (or complex) variable, then for every sequence t of real (or complex) numbers, s**t is a sequence of polynomials p(n) in x, and the zeros of p(n) are the numbers -t(0), -t(1), ..., -t(n).
Following are abbreviations in the guide below for triples (s, t, s**t):
F = (0,1,1,2,3,5,...) = A000045, Fibonacci numbers
L = (2,1,3,4,7,11,...) = A000032, Lucas numbers
P = (2,3,5,7,11,...) = A000040, primes
T = (1,3,6,10,15,...) = A000217, triangular numbers
C = (1,2,6,20,70, ...) = A000984, central binomial coefficients
LW = (1,3,4,6,8,9,...) = A000201, lower Wythoff sequence
UW = (2,5,7,10,13,...) = A001950, upper Wythoff sequence
[ ] = floor
In the guide below, sequences s**t are identified with index numbers Axxxxxx; in some cases, s**t and Axxxxxx differ in one or two initial terms.
Table 1. s = A000012 = (1,1,1,1...) = (1);
t = A000012; 1                 s**t = A000079; 2^(n+1)
t = A000027; n                 s**t = A000142; (n+1)!
t = A000040, P                 s**t = A054640
t = A000040, P           (1/3) s**t = A374852
t = A000079, 2^n               s**t = A028361
t = A000079, 2^n         (1/3) s**t = A028362
t = A000045, F                 s**t = A082480
t = A000032, L                 s**t = A374890
t = A000201, LW                s**t = A374860
t = A001950, UW                s**t = A374864
t = A005408, 2*n+1             s**t = A000165, 2^n*n!
t = A016777, 3*n+1             s**t = A008544
t = A016789, 3*n+2             s**t = A032031
t = A000142, n!                s**t = A217757
t = A000051, 2^n+1             s**t = A139486
t = A000225, 2^n-1             s**t = A006125
t = A032766, [3*n/2]           s**t = A111394
t = A034472, 3^n+1             s**t = A153280
t = A024023, 3^n-1             s**t = A047656
t = A000217, T                 s**t = A128814
t = A000984, C                 s**t = A374891
t = A279019, n^2-n             s**t = A130032
t = A004526, 1+[n/2]           s**t = A010551
t = A002264, 1+[n/3]           s**t = A264557
t = A002265, 1+[n/4]           s**t = A264635
Sequences (c)**L, for c=2..4: A374656 to A374661
Sequences (c)**F, for c=2..6: A374662, A374662, A374982 to A374855
The obverse convolutions listed in Table 1 are, trivially, divisibility sequences. Likewise, if s = (-1,-1,-1,...) instead of s = (1,1,1,...), then s**t is a divisibility sequence for every choice of t; e.g. if s = (-1,-1,-1,...) and t = A279019, then s**t = A130031.
Table 2. s = A000027 = (0,1,2,3,4,5,...) = (n);
t = A000027, n                 s**t = A007778, n^(n+1)
t = A000290, n^2               s**t = A374881
t = A000040, P                 s**t = A374853
t = A000045, F                 s**t = A374857
t = A000032, L                 s**t = A374858
t = A000079, 2^n               s**t = A374859
t = A000201, LW                s**t = A374861
t = A005408, 2*n+1             s**t = A000407, (2*n+1)! / n!
t = A016777, 3*n+1             s**t = A113551
t = A016789, 3*n+2             s**t = A374866
t = A000142, n!                s**t = A374871
t = A032766, [3*n/2]           s**t = A374879
t = A000217, T                 s**t = A374892
t = A000984, C                 s**t = A374893
t = A038608, n*(-1)^n          s**t = A374894
Table 3. s = A000290 = (0,1,4,9,16,...) = (n^2);
t = A000290, n^2               s**t = A323540
t = A002522, n^2+1             s**t = A374884
t = A000217, T                 s**t = A374885
t = A000578, n^3               s**t = A374886
t = A000079, 2^n               s**t = A374887
t = A000225, 2^n-1             s**t = A374888
t = A005408, 2*n+1             s**t = A374889
t = A000045, F                 s**t = A374890
Table 4. s = t;
s = t = A000012, 1             s**s = A000079; 2^(n+1)
s = t = A000027, n             s**s = A007778, n^(n+1)
s = t = A000290, n^2           s**s = A323540
s = t = A000045, F             s**s = this sequence
s = t = A000032, L             s**s = A374850
s = t = A000079, 2^n           s**s = A369673
s = t = A000244, 3^n           s**s = A369674
s = t = A000040, P             s**s = A374851
s = t = A000201, LW            s**s = A374862
s = t = A005408, 2*n+1         s**s = A062971
s = t = A016777, 3*n+1         s**s = A374877
s = t = A016789, 3*n+2         s**s = A374878
s = t = A032766, [3*n/2]       s**s = A374880
s = t = A000217, T             s**s = A375050
s = t = A005563, n^2-1         s**s = A375051
s = t = A279019, n^2-n         s**s = A375056
s = t = A002398, n^2+n         s**s = A375058
s = t = A002061, n^2+n+1       s**s = A375059
If n = 2*k+1, then s**s(n) is a square; specifically,
s**s(n) = ((s(0)+s(n))*(s(1)+s(n-1))*...*(s(k)+s(k+1)))^2.
If n = 2*k, then s**s(n) has the form 2*s(k)*m^2, where m is an integer.
Table 5. Others
s = A000201, LW      t = A001950, UW         s**t = A374863
s = A000045, F       t = A000032, L          s**t = A374865
s = A005843, 2*n     t = A005408, 2*n+1      s**t = A085528, (2*n+1)^(n+1)
s = A016777, 3*n+1   t = A016789, 3*n+2      s**t = A091482
s = A005408, 2*n+1   t = A000045, F          s**t = A374867
s = A005408, 2*n+1   t = A000032, L          s**t = A374868
s = A005408, 2*n+1   t = A000079, 2^n        s**t = A374869
s = A000027, n       t = A000142, n!         s**t = A374871
s = A005408, 2*n+1   t = A000142, n!         s**t = A374872
s = A000079, 2^n     t = A000142, n!         s**t = A374874
s = A000142, n!      t = A000045, F          s**t = A374875
s = A000142, n!      t = A000032, L          s**t = A374876
s = A005408, 2*n+1   t = A016777, 3*n+1      s**t = A352601
s = A005408, 2*n+1   t = A016789, 3*n+2      s**t = A064352
Table 6. Arrays of coefficients of s(x)**t(x), where s(x) and t(x) are polynomials
s(x)              t(x)            s(x)**t(x)
 n                 x              A132393
n^2                x              A269944
x+1               x+1             A038220
x+2               x+2             A038244
 x                x+3             A038220
nx                x+1             A094638
 1              x^2+x+1           A336996
n^2 x             x+1             A375041
n^2 x            2x+1             A375042
n^2 x             x+2             A375043
2^n x             x+1             A375044
2^n              2x+1             A375045
2^n              x+2              A375046
x+1              F(n)             A375047
x+1             x+F(n)            A375048
x+F(n)          x+F(n)            A375049

			a(0) = 0 + 0 = 0
a(1) = (0+1) * (1+0) = 1
a(2) = (0+1) * (1+1) * (1+0) = 2
a(3) = (0+2) * (1+1) * (1+1) * (2+0) = 16
As noted above, a(2*k+1) is a square for k>=0. The first 5 squares are 1, 16, 3600, 12320100, 701841817600, with corresponding square roots 1, 4, 60, 3510, 837760.
If n = 2*k, then s**s(n) has the form 2*F(k)*m^2, where m is an integer and F(k) is the k-th Fibonacci number; e.g., a(6) = 2*F(3)*(192)^2.

Cf. A000045, A374850-to-A374881, A374884-to-A374894, A375041-to-A375049.

a:= n-> (F-> mul(F(n-j)+F(j), j=0..n))(combinat[fibonacci]):
seq(a(n), n=0..15);  # Alois P. Heinz, Aug 02 2024

s[n_] := Fibonacci[n]; t[n_] := Fibonacci[n];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}];
Table[u[n], {n, 0, 20}]

a(n)=prod(k=0, n, fibonacci(k) + fibonacci(n-k)) \\ Andrew Howroyd, Jul 31 2024

a(n) ~ c * phi^(3*n^2/4 + n) / 5^((n+1)/2), where c = QPochhammer(-1, 1/phi^2)^2/2 if n is even and c = phi^(1/4) * QPochhammer(-phi, 1/phi^2)^2 / (phi + 1)^2 if n is odd, and phi = A001622 is the golden ratio. - Vaclav Kotesovec, Aug 01 2024

A085527 a(n) = (2n+1)^n.

Original entry on oeis.org

1, 3, 25, 343, 6561, 161051, 4826809, 170859375, 6975757441, 322687697779, 16679880978201, 952809757913927, 59604644775390625, 4052555153018976267, 297558232675799463481, 23465261991844685929951, 1977985201462558877934081, 177482997121587371826171875

Offset: 0

N. J. A. Sloane, Jul 05 2003

a(n) is the determinant of the zigzag matrix Z(n) (see A088961). - Paul Boddington, Nov 03 2003
a(n) is also the number of rho-labeled graphs with n edges. A graph with n edges is a rho-labeled graph if there exists a one-to-one mapping from its vertex set to {0,1,...,2n} such that every edge receives as a label the absolute difference of its end-vertices and the edge labels are x1,x2,...,xn where xi=i or xi=2n+1-i. - Christian Barrientos and Sarah Minion, Feb 20 2015
a(n) is the number of nodes in the canonical automaton for the affine Weyl group of types B_n and C_n. - Tom Edgar, May 12 2016
a(n) is the number of rooted (at an edge) 2-trees with n+2 edges. See also A052750. - Nikos Apostolakis, Dec 05 2018

Anders Björner and Francesco Brenti, Combinatorics of Coxeter groups. Graduate Texts in Mathematics, 231. Springer, New York, 2005.

G. C. Greubel, Table of n, a(n) for n = 0..350
Karola Mészáros, Labeling the Regions of the Type C_n Shi Arrangement, The Electronic Journal of Combinatorics, vol. 20, no. 2, (2013).
Zhi-Wei Sun, Fedor Petrov, A surprising identity, MathOverflow, Jan 17 2019.

Cf. A062971, A085528, A088961, A099753, A214406, A052750.

List([0..20],n->(2*n+1)^n); # Muniru A Asiru, Dec 05 2018

[(2*n+1)^n: n in [0..20]]; // Wesley Ivan Hurt, Mar 01 2015

A085527:=n->(2*n+1)^n: seq(A085527(n), n=0..20); # Wesley Ivan Hurt, Mar 01 2015

Table[(2 n + 1)^n, {n, 0, 20}] (* Wesley Ivan Hurt, Mar 01 2015 *)

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

def A085527(n): return ((n<<1)|1)**n # Chai Wah Wu, Nov 10 2024

E.g.f.: sqrt(2)/(2*(1+LambertW(-2*x))*sqrt(-x/LambertW(-2*x))). - Vladeta Jovovic, Oct 16 2004
For r = 0, 1, 2, ..., the e.g.f. for the sequence whose n-th term is (2*n+1)^(n+r) can be expressed in terms of the function U(z) = Sum_{n >= 0} (2*n+1)^(n-1)*z^(2*n+1)/(2^n*n!). See A214406 for details. In the present case, r = 0, and the resulting e.g.f. is 1/z*U(z)/(1 - U(z)^2) taken at z = sqrt(2*x). - Peter Bala, Aug 06 2012
a(n) = [x^n] 1/(1 - (2*n+1)*x). - Ilya Gutkovskiy, Oct 10 2017
a(n) = (-2)^n * D(2*n + 1), where D(n) is the determinant of the n X n matrix M with elements M(j, k) = cos(Pi*j*k/n). See the Zhi-Wei Sun, Petrov link. - Peter Luschny, Sep 19 2021
a(n) ~ exp(1/2) * 2^n * n^n. - Vaclav Kotesovec, Dec 05 2021
Series reversion of (1 - x)^2 * log(1/(1 - x)) begins  x + 3*x^2/2! + 25*x^3/3! + 343*x^4/4! + 6561*x^5/5! + .... - Peter Bala, Sep 27 2023
a(n) = Product_{k=1..n} tan(k*Pi/(1+2*n))^(2*n). - Chai Wah Wu, Nov 10 2024

A085534 a(n) = (2n)^(2n).

Original entry on oeis.org

1, 4, 256, 46656, 16777216, 10000000000, 8916100448256, 11112006825558016, 18446744073709551616, 39346408075296537575424, 104857600000000000000000000, 341427877364219557396646723584, 1333735776850284124449081472843776, 6156119580207157310796674288400203776

Offset: 0

N. J. A. Sloane, Jul 05 2003

nonn

All terms are both perfect squares and numbers of the form n^n. - William Boyles, Jul 31 2015
Intersection of A000290 and A000312. - Michel Marcus, Aug 04 2015
Intersection of A005843 and A000312. - Robert Israel, Aug 04 2015
The number of sequences of length 2n using 2n symbols. - Washington Bomfim, Jan 14 2020

Alois P. Heinz, Table of n, a(n) for n = 0..100

Cf. A000312, A073009, A083648, A085529.

Column k=0 of A246070.

{1}~Join~Table[(2 n)^(2 n), {n, 1, 4!}] (* Michael De Vlieger, Aug 04 2015 *)

def A085534(n): return (m:=n<<1)**m # Chai Wah Wu, Nov 18 2022

a(n) = A000312(2*n). - Michel Marcus, Jul 31 2015
a(n) = A062971(n)^2. - Michel Marcus, Aug 04 2015
a(n) = [x^(2*n)] 1/(1 - 2*n*x). - Ilya Gutkovskiy, Oct 10 2017
Sum_{n>=0} 1/a(n) = 1 + (A073009-A083648)/2 = 1.2539277431... . - Amiram Eldar, May 17 2022

A246070 Number A(n,k) of endofunctions f on [2n] satisfying f^k(i) = i for all i in [n]; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

1, 1, 4, 1, 2, 256, 1, 3, 16, 46656, 1, 2, 50, 216, 16777216, 1, 3, 36, 1626, 4096, 10000000000, 1, 2, 56, 1440, 83736, 100000, 8916100448256, 1, 3, 16, 2688, 84624, 6026120, 2985984, 11112006825558016, 1, 2, 70, 720, 215760, 7675200, 571350096, 105413504, 18446744073709551616

Offset: 0

Alois P. Heinz, Aug 12 2014

			Square array A(n,k) begins:
0 :            1,      1,       1,       1,        1,        1, ...
1 :            4,      2,       3,       2,        3,        2, ...
2 :          256,     16,      50,      36,       56,       16, ...
3 :        46656,    216,    1626,    1440,     2688,      720, ...
4 :     16777216,   4096,   83736,   84624,   215760,    94816, ...
5 :  10000000000, 100000, 6026120, 7675200, 24899120, 11218000, ...

Alois P. Heinz, Antidiagonals n = 0..70, flattened

Columns k=0-3 give: A085534, A062971, A245141, A245959.
Main diagonal gives A246071.
Cf. A246072 (the same for permutations).

with(numtheory): with(combinat): M:=multinomial:
b:= proc(n, k, p) local l, g; l, g:= sort([divisors(p)[]]),
      proc(k, m, i, t) option remember; local d, j; d:= l[i];
        `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
         (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
        `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
        `if`(t=0, [][], m/t))))
      end; g(k, n-k, nops(l), 0)
    end:
A:= (n, k)-> `if`(k=0, (2*n)^(2*n), b(2*n, n, k)):
seq(seq(A(n, d-n), n=0..d), d=0..10);

multinomial[n_, k_List] := n!/Times @@ (k!); M = multinomial;
b[n_, k0_, p_] := Module[{l, g}, l = Divisors[p];
g[k_, m_, i_, t_] := g[k, m, i, t] = Module[{d, j}, d = l[[i]];
    If[i == 1, If[m == 0, 1, n^m], Sum[M[k, Join[{k - (d - t)*j},
    Table[d - t, {j}]]]/j!*If[j == 0, 1, (d - 1)!^j]*M[m, Join[{m - t*j},
    Array[t&, j]]]*g[k - (d - t)*j, m - t*j, Sequence @@
    If[d - t == 1, {i - 1, 0}, {i, t + 1}]], {j, 0, Min[k/(d - t),
    If[t == 0, {}, m/t]]}]]];
g[k0, n - k0, Length[l], 0]];
A[n_, k_] := If[k == 0, If[n == 0, 1, (2n)^(2n)], b[2*n, n, k]];
Table[A[n, d - n], {d, 0, 10}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 27 2016, after Alois P. Heinz, updated Jan 01 2021 *)

A066642 a(n) = floor(n^(n/2)).

Original entry on oeis.org

1, 1, 2, 5, 16, 55, 216, 907, 4096, 19683, 100000, 534145, 2985984, 17403307, 105413504, 661735513, 4294967296, 28761784747, 198359290368, 1406563064942, 10240000000000, 76436817165460, 584318301411328, 4569515072723572, 36520347436056576, 298023223876953125

Offset: 0

Amarnath Murthy, Dec 29 2001

			a(5) = 55 as {5^(1/2)}^5 = 55.9016994374947424102293417182819...

Alois P. Heinz, Table of n, a(n) for n = 0..702 (terms n=1..150 from Harry J. Smith)

Cf. A092503, A147771, A190343.

Bisection gives A062971 (even part).

[Floor(n^(n/2)): n in [1..25]]; // G. C. Greubel, Dec 30 2017

a:= n-> floor(n^(n/2)):
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 08 2025

Mathematica
```
Table[ Floor[Sqrt[n]^n], {n, 1, 25} ]
```

a(n) = sqrtint(n^n); \\ Michel Marcus, Nov 01 2022

from math import isqrt
def A066642(n): return isqrt(n**n) # Chai Wah Wu, Jun 08 2025

More terms from Robert G. Wilson v, Jan 03 2002

a(0)=1 prepended by Alois P. Heinz, Jun 08 2025

A003167 Number of n-dimensional cuboids with integral edge lengths for which volume = surface area.

Original entry on oeis.org

2, 10, 108, 2892, 270332

Offset: 2

mjzerger(AT)adams.edu

For n>1 it is always true that a(n) > 0 because for dimension n we always have the n-dimensional cuboid with all edge lengths = 2n = A062971(n) having hypervolume (2n)^n equal to "surface hyper-area". - Jonathan Vos Post, Mar 15 2006

Number of nondecreasing tuples (x_1, x_2, ..., x_n) such that 1/2 = 1/x_1 + 1/x_2 + ... + 1/x_n. - Lewis Chen, Dec 20 2019

			From _Joseph Myers_, Feb 24 2004: (Start)
For n=2 the cuboids are 3 X 6 and 4 X 4.
For n=3 the cuboids are 3 X 7 X 42, 3 X 8 X 24, 3 X 9 X 18, 3 X 10 X 15, 3 X 12 X 12, 4 X 5 X 20, 4 X 6 X 12, 4 X 8 X 8, 5 X 5 X 10, 6 X 6 X 6. (End)
For n=4 see the Marcus link.

Gerald E. Gannon, Martin V. Bonsangue and Terrence J. Redfern, One Good Problem Leads to Another and Another and..., Math. Teacher, 90 (#3, 1997), pp. 188-191.
Michel Marcus, Cuboids for n=4, after Joseph Myers.

Cf. A002966.

a(5)-a(6) from Joseph Myers, Feb 24 2004

A091482 a(n) = (3*n)^n.

Original entry on oeis.org

1, 3, 36, 729, 20736, 759375, 34012224, 1801088541, 110075314176, 7625597484987, 590490000000000, 50542106513726817, 4738381338321616896, 482880748567480579719, 53148384174432398229504, 6283298708943145751953125, 794071845499378503449051136

Offset: 0

Christian G. Bower, Jan 13 2004

Cf. A062971, A091483.

[(3*n)^n : n in [0..20]]; // Zaki Khandaker, Jun 21 2015

Join[{1}, Table[(3 n)^n, {n, 20}]] (* Vincenzo Librandi, Jun 21 2015 *)

a(n) = (3*n)^n \\ Charles R Greathouse IV, Jun 21 2015

E.g.f.: 1/(1 + LambertW(-3*x)). - Ilya Gutkovskiy, Oct 03 2017

A349962 a(n) = Sum_{k=0..n} (2*k)^k.

Original entry on oeis.org

1, 3, 19, 235, 4331, 104331, 3090315, 108503819, 4403471115, 202762761483, 10442762761483, 594761064172811, 37115108500229387, 2518267981703965963, 184577387811646500107, 14533484387811646500107, 1223459304002440821206283, 109651494909968373175414027

Offset: 0

Seiichi Manyama, Dec 07 2021

Partial sums of A062971.

Seiichi Manyama, Table of n, a(n) for n = 0..351

Cf. A062970, A062971, A349961, A349963, A349970.

a[n_] := Sum[If[k == 0, 1, (2*k)^k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Dec 07 2021 *)

PARI
```
a(n) = sum(k=0, n, (2*k)^k);
```

a(n) ~ 2^n * n^n. - Vaclav Kotesovec, Dec 07 2021

A091483 a(n) = (4*n)^n.

Original entry on oeis.org

1, 4, 64, 1728, 65536, 3200000, 191102976, 13492928512, 1099511627776, 101559956668416, 10485760000000000, 1196683881290399744, 149587343098087735296, 20325604337285010030592, 2982856619293778479415296, 470184984576000000000000000

Offset: 0

Christian G. Bower, Jan 13 2004

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Cf. A062971, A091482.

[(4*n)^n: n in [0..20]]; // Vincenzo Librandi, Feb 24 2014

Join[{1},Table[(4n)^n,{n,20}]] (* Harvey P. Dale, Feb 11 2024 *)

a(n) = (4*n)^n; \\ Joerg Arndt, Feb 23 2014

E.g.f.: 1/(1 + LambertW(-4*x)). - Ilya Gutkovskiy, Oct 03 2017

More terms from Vincenzo Librandi, Feb 24 2014

A092175 Define d(n,k) to be the number of '1' digits required to write out all the integers from 1 through k in base n. E.g., d(10,9) = 1 (just '1'), d(10,10) = 2 ('1' and '10'), d(10,11) = 4 ('1', '10' and '11'). Then a(n) is the first k >= 1 such that d(n,k) > k.

Original entry on oeis.org

2, 3, 13, 29, 182, 427, 3931, 8185, 102781, 199991, 3179143, 5971957, 114818731, 210826995, 4754446861, 8589934577, 222195898594, 396718580719, 11575488191148, 20479999999981, 665306762187614, 1168636602822635, 41826814261329723, 73040694872113129

Offset: 1

Ken Bateman (kbateman(AT)erols.com) and Graeme McRae, Apr 01 2004

The number of video tapes you can label sequentially starting with "1" using the n different number stickers that come in the box, working in base n.

Adapted from puzzle described in the Ponder This web page.

			John Fletcher gives the following treatment of the case of odd B at the 'solutions' link: a(10)=199991 because you can label 199990 tapes using 199990 sets of base-10 sticky digit labels, but the 199991st tape can't be labeled with 199991 sets of sticky digit labels.

Michael Brand was the originator of the problem.

Gregory Marton, Table of n, a(n) for n = 1..100
IBM Corp., April 2004 "Ponder This" challenge.
IBM Corp., April 2004 "Ponder This" solutions.

Cf. A062971.

When n is even, a(n) = 2*n^(n/2) - n + 1.

Edited by Robert G. Wilson v, based on comments from Don Coppersmith and John Fletcher, May 11 2004

a(13) corrected and a(23) onwards added by Gregory Marton, Jul 29 2023

cp's OEIS Frontend

A374848 Obverse convolution A000045**A000045; see Comments.

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A085527 a(n) = (2n+1)^n.

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A085534 a(n) = (2n)^(2n).

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A246070 Number A(n,k) of endofunctions f on [2n] satisfying f^k(i) = i for all i in [n]; square array A(n,k), n>=0, k>=0, read by antidiagonals.

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A066642 a(n) = floor(n^(n/2)).

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A003167 Number of n-dimensional cuboids with integral edge lengths for which volume = surface area.

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A091482 a(n) = (3*n)^n.

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