A360817 Expansion of Sum_{k>=0} (k*x)^(3*k) / (1 - k*x)^(k+1).

1, 0, 0, 1, 2, 3, 68, 389, 1542, 24810, 251564, 1814487, 27520734, 391640548, 4295115396, 69305652406, 1221344986380, 18207710383335, 329699350020676, 6759819628538561, 126950556666301050, 2624697847966227077, 60825028694289947940, 1365568620213461601924

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..449

Formula

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

Prog

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

Crossrefs

Cf. A072034, A360816.

Cf. A360815.

Sequence in context: A365504 A041249 A356795 * A184949 A132598 A257173

Adjacent sequences: A360814 A360815 A360816 * A360818 A360819 A360820

Keyword

nonn

Author

Seiichi Manyama, Feb 21 2023

Status

approved