A361835 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(n*k,n-k).

1, 2, 2, -10, -10, 242, -678, -7054, 88342, -207646, -6015904, 88310862, -312514816, -8847633338, 184252541514, -1269592841970, -17662739133178, 634109114537218, -7914500471718552, -18165019012117450, 2936604063787679650, -62899139815867627378

Offset: 0

Author

Seiichi Manyama, Mar 26 2023

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 0..481

Crossrefs

Main diagonal of A361834.

Cf. A361829, A361836.

Programs

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*binomial(2*k, k)*binomial(n*k, n-k));

Formula

a(n) = [x^n] 1/sqrt(1 - 4*x*(1-x)^n).