A328812 Constant term in the expansion of (Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n.

1, 2, 10, 164, 9826, 2031252, 1622278624, 4579408029576, 51207103076632066, 2052124795850957537060, 330463219813679264204224300, 192454957455454582636391397662856, 454577215426865313388106323928590128736, 3907905904547764847197154889183844343802986600

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..58

Formula

a(n) = A309010(n,n+1) = Sum_{k=0..n} binomial(n,k)^(n+1).

a(n) ~ c * exp(-1/4) * 2^((2*n+1)*(n+1)/2) / (Pi*n)^((n+1)/2), where c = A218792 = Sum_{k = -infinity..infinity} exp(-2*k^2) = 1.271341522189... and c = Sum_{k = -infinity..infinity} exp(-2*(k+1/2)^2) = 1.23528676585389... if n is odd. - Vaclav Kotesovec, May 06 2021

Mathematica

a[n_] := Sum[Binomial[n, k]^(n + 1), {k, 0, n}]; Array[a, 14, 0] (* Amiram Eldar, May 06 2021 *)

Prog

(PARI) {a(n) = sum(k=0, n, binomial(n, k)^(n+1))}

Crossrefs

Cf. A167010, A309010, A328813, A328814.

Sequence in context: A294352 A007131 A126449 * A126451 A260122 A132341

Adjacent sequences: A328809 A328810 A328811 * A328813 A328814 A328815

Keyword

nonn

Author

Seiichi Manyama, Oct 28 2019

Status

approved