A360835 Expansion of Sum_{k>=0} (k * x)^k / (1 - (k * x)^3)^(k+1).
1, 1, 4, 27, 258, 3221, 49572, 905466, 19122502, 458161191, 12275530636, 363646493044, 11801356347294, 416365459777150, 15867258718677348, 649548679156603983, 28426564854590132236, 1324406974148881529057, 65448443631801436742052
Offset: 0
Keywords
Programs
-
PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-(k*x)^3)^(k+1))) -
PARI
a(n) = sum(k=0, n\3, (n-3*k)^n*binomial(n-2*k, k));
Formula
a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^n * binomial(n-2*k,k).