A361814 Expansion of 1/sqrt(1 - 4*x*(1+x)^5).

1, 2, 16, 100, 660, 4482, 30886, 215364, 1515000, 10730800, 76426846, 546792056, 3926775646, 28290272420, 204375145480, 1479963148220, 10739326203132, 78072933869364, 568503202324540, 4145718464390120, 30271771382355430, 221305746414518180

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..1139

Formula

a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(5*k,n-k).

n*a(n) = 2 * ( (2*n-1)*a(n-1) + 5*(2*n-2)*a(n-2) + 10*(2*n-3)*a(n-3) + 10*(2*n-4)*a(n-4) + 5*(2*n-5)*a(n-5) + (2*n-6)*a(n-6) ) for n > 5.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1+x)^5))
(PARI) a(n)= sum(k=0, n, binomial(2*k, k) * binomial(5*k, n-k)) \\ Winston de Greef, Mar 25 2023

Crossrefs

Cf. A006139, A137635, A360133, A361790, A361791, A361792, A361812, A361813.

Sequence in context: A319603 A043016 A197202 * A032260 A197800 A209645

Adjacent sequences: A361811 A361812 A361813 * A361815 A361816 A361817

Keyword

nonn

Author

Seiichi Manyama, Mar 25 2023

Status

approved