A360815 - OEIS

%I #10 Feb 22 2023 10:19:58

%S 1,0,0,1,2,3,5,11,30,88,260,771,2343,7474,25380,91650,347988,1371873,

%T 5570173,23233703,99676434,440931977,2014619700,9506385864,

%U 46246356169,231348803925,1187212953132,6239006165820,33546182775824,184497923546700

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

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

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

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

%Y Cf. A360709.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Feb 21 2023