A348321 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n*(n-k),n*k).

1, 1, 0, -19, -493, -12500, 2110381, 2291797033, 2190576317924, 641690166054149, -51808237792071009216, -1670420776971967146820397, -51706433129693385388017540008, 3622699946475084834038607930411332, 5598748000229343046813449019221837072281

Offset: 0

Author

Seiichi Manyama, Oct 12 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..69

Crossrefs

Cf. A238696, A348322.

Programs

Mathematica

a[n_] := Sum[(-1)^k * Binomial[n*(n - k), n*k], {k, 0, n}]; Array[a, 15, 0] (* Amiram Eldar, Oct 12 2021 *)

PARI

a(n) = sum(k=0, n, (-1)^k*binomial(n*(n-k), n*k));

PARI

a(n) = if(n==0, 1, polcoef((1-x)^(n-1)/((1-x)^n+x^(2*n)+x*O(x^n^2)), n^2));

Formula

a(n) = [x^(n^2)] (1-x)^(n-1)/((1-x)^n + x^(2*n)) for n > 0.