A348322 a(n) = Sum_{k=0..n} (-1)^k * binomial(n^2 - k,n*k).

1, 1, -2, -48, 1626, 931040, -479909170, -5499596761127, 43158334880135692, 9081843551946977373216, -1095541637114516172591381711, -4049135740387789992460066844854898, 7569951149407063102291625516677078697579

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..57

Formula

a(n) = [x^(n^2)] (1-x)^(n-1)/((1-x)^n + x^(n+1)).

Mathematica

a[n_] := Sum[(-1)^k * Binomial[n^2 - k, n*k], {k, 0, n}]; Array[a, 13, 0] (* Amiram Eldar, Oct 12 2021 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n^2-k, n*k));
(PARI) a(n) = polcoef((1-x)^(n-1)/((1-x)^n+x^(n+1)+x*O(x^n^2)), n^2);

Crossrefs

Cf. A078001, A348315, A348321.

Sequence in context: A010046 A013517 A027509 * A186284 A119695 A119698

Adjacent sequences: A348319 A348320 A348321 * A348323 A348324 A348325

Keyword

sign

Author

Seiichi Manyama, Oct 12 2021

Status

approved