A360788 Expansion of Sum_{k>=0} x^k / (1 - (k*x)^3)^(k+1).
1, 1, 1, 1, 3, 25, 109, 324, 1135, 8803, 64189, 337854, 1707319, 13421410, 121248893, 894378619, 6082868725, 53046554917, 543432115477, 4989423130739, 42565774604131, 421544374075072, 4781440892689533, 51342685464272591, 522295380717090265
Offset: 0
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^3)^(k+1))) -
PARI
a(n) = sum(k=0, n\3, (n-3*k)^(3*k)*binomial(n-2*k, k));
Formula
a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^(3*k) * binomial(n-2*k,k).