A360817 - OEIS

%I #14 Jan 09 2024 08:46:29

%S 1,0,0,1,2,3,68,389,1542,24810,251564,1814487,27520734,391640548,

%T 4295115396,69305652406,1221344986380,18207710383335,329699350020676,

%U 6759819628538561,126950556666301050,2624697847966227077,60825028694289947940,1365568620213461601924

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

%H Seiichi Manyama, <a href="/A360817/b360817.txt">Table of n, a(n) for n = 0..449</a>

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^(3*k)/(1-k*x)^(k+1)))

%o (PARI) a(n) = sum(k=0, n\3, k^n*binomial(n-2*k, k));

%Y Cf. A072034, A360816.

%Y Cf. A360815.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Feb 21 2023