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

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Main diagonal of A361834.

Cf. A361829, A361836.

Sequence in context: A147801 A367545 A263053 * A066965 A066966 A132443

Adjacent sequences: A361832 A361833 A361834 * A361836 A361837 A361838

Keyword

sign

Author

Seiichi Manyama, Mar 26 2023

Status

approved