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A328813 Constant term in the expansion of (-1 + Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n. 4

%I

%S 1,1,7,115,8071,1770951,1505946121,4368457532265,49949721645153751,

%T 2021436054924485283799,327902645022367779788597977,

%U 191573267131797606250658812550565,453516825886934673673734108656254582801

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

%H Seiichi Manyama, <a href="/A328813/b328813.txt">Table of n, a(n) for n = 0..58</a>

%F a(n) = A328747(n,n+1) = Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^(n+1).

%t a[n_] := Sum[(-1)^(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 *)

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

%Y Cf. A328747, A328812, A328814.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 28 2019

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)