A360292 a(n) = Sum_{k=0..floor(n/4)} binomial(n-1-3*k,k) * binomial(2*n-8*k,n-4*k).

1, 2, 6, 20, 70, 254, 936, 3492, 13150, 49882, 190318, 729576, 2807816, 10841962, 41983588, 162973568, 633994982, 2471010742, 9646981054, 37718873700, 147676286078, 578883674722, 2271704404900, 8923807316892, 35087269756344, 138075819924306

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1 / sqrt(1-4*x/(1-x^4)).

n*a(n) = 2*(2*n-1)*a(n-1) + 2*(n-4)*a(n-4) - 2*(2*n-13)*a(n-5) - (n-8)*a(n-8).

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n-1-3*k, k)*binomial(2*n-8*k, n-4*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^4)))

Crossrefs

Cf. A085362, A360290, A360291.

Cf. A360295.

Sequence in context: A000984 A087433 A119373 * A151284 A049138 A095929

Adjacent sequences: A360289 A360290 A360291 * A360293 A360294 A360295

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2023

Status

approved