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A328814 Constant term in the expansion of (-2 + Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n. 4
1, 0, 6, 72, 6690, 1536000, 1398496680, 4165565871600, 48724656010825410, 1991141239554487077120, 325362786100184356140612996, 190695111051826003327799496771600, 452459020719698368348441955010421696800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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).

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 *)

PROG

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

CROSSREFS

Cf. A328748, A328812, A328813.

Sequence in context: A006585 A166472 A182917 * A203433 A008562 A041063

Adjacent sequences:  A328811 A328812 A328813 * A328815 A328816 A328817

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 28 2019

STATUS

approved

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Last modified November 29 01:40 EST 2021. Contains 349416 sequences. (Running on oeis4.)