A360709 Expansion of Sum_{k>=0} (x^3 / (1 - k*x))^k.

1, 0, 0, 1, 1, 1, 2, 5, 13, 34, 90, 247, 720, 2256, 7568, 26814, 98982, 377541, 1484254, 6021789, 25271173, 109850447, 494355359, 2298362532, 11008133629, 54175202125, 273460921605, 1414449612648, 7494262602464, 40669492399396

Offset

0,7

Links

Winston de Greef, Table of n, a(n) for n = 0..692

Formula

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

Prog

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

Crossrefs

Cf. A080108, A360708.

Cf. A078012, A360707.

Sequence in context: A023425 A304173 A217896 * A090827 A109192 A192313

Adjacent sequences: A360706 A360707 A360708 * A360710 A360711 A360712

Keyword

nonn

Author

Seiichi Manyama, Feb 17 2023

Status

approved