A328814 Constant term in the expansion of (-2 + Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n.

1, 0, 6, 72, 6690, 1536000, 1398496680, 4165565871600, 48724656010825410, 1991141239554487077120, 325362786100184356140612996, 190695111051826003327799496771600, 452459020719698368348441955010421696800

Offset: 0

Author

Seiichi Manyama, Oct 28 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A328748, A328812, A328813.

Programs

Mathematica

a[n_] := Sum[(-2)^(n-i) * Binomial[n, i] * Sum[Binomial[i, j]^(n+1), {j, 0, i}], {i, 0, n}]; Array[a, 13, 0] (* Amiram Eldar, May 06 2021 *)

PARI

{a(n) = sum(i=0, n, (-2)^(n-i)*binomial(n, i)*sum(j=0, i, binomial(i, j)^(n+1)))}

Formula

a(n) = A328748(n,n+1) = Sum_{i=0..n} (-2)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^(n+1).