A368898 - OEIS

A368898

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

1, 1, 1, 1, 5, 11, 19, 29, 105, 298, 671, 1299, 3997, 12468, 33083, 75781, 220625, 708867, 2086183, 5412778, 15756741, 51093316, 160523859, 457283931, 1365001273, 4458076176, 14608351135, 44649287452, 137979763181, 455582050840, 1536403659211, 4953147876189

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..31.

FORMULA

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

a(n) = hypergeom([(1-n)/4, (2-n)/4, (3-n)/4, -n/4], [(1-n)/3, (2-n)/3, -n/3], -256*n/27). - Stefano Spezia, Jan 09 2024

a(n) ~ (1/4) * exp(n^(3/4)/4 + sqrt(n)/16 + 5*n^(1/4)/384) * n^(n/4) * (1 + 30643/(40960*n^(1/4)) + 3749229947/(10066329600*sqrt(n)) + 15892274778169/(137438953472000*n^(3/4))). - Vaclav Kotesovec, Jan 09 2024

MATHEMATICA

Table[HypergeometricPFQ[{1/4 - n/4, 1/2 - n/4, 3/4 - n/4, -n/4}, {1/3 - n/3, 2/3 - n/3, -n/3}, -256*n/27], {n, 0, 20}] (* Vaclav Kotesovec, Jan 09 2024 *)

PROG

(PARI) a(n) = sum(k=0, n\4, n^k*binomial(n-3*k, k));

CROSSREFS

Cf. A171180, A368891.

Sequence in context: A045451 A338566 A352795 * A326665 A100920 A274946

Adjacent sequences: A368895 A368896 A368897 * A368899 A368900 A368901

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jan 09 2024

STATUS

approved