A360295 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-1-3*k,k) * binomial(2*n-8*k,n-4*k).

1, 2, 6, 20, 70, 250, 912, 3372, 12590, 47362, 179230, 681528, 2601896, 9966798, 38288420, 147453664, 569092438, 2200577502, 8523612766, 33064771524, 128438624798, 499525018638, 1944918241388, 7580283784548, 29571439970136, 115459524588322, 451157870454298

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, (-1)^k*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. A360293, A360294.

Sequence in context: A193653 A147748 A150125 * A224514 A065345 A130914

Adjacent sequences: A360292 A360293 A360294 * A360296 A360297 A360298

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2023

Status

approved