A360749 Expansion of Sum_{k>=0} (x * (1 + k*x^3))^k.
1, 1, 1, 1, 2, 5, 10, 17, 30, 64, 146, 315, 649, 1386, 3164, 7381, 16931, 38649, 90406, 217474, 527586, 1277452, 3112371, 7705059, 19336789, 48800634, 123617380, 315671212, 814711955, 2119996540, 5545342621, 14584694613, 38641783669, 103158314515
Offset: 0
Keywords
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (x*(1+k*x^3))^k)) -
PARI
a(n) = sum(k=0, n\4, (n-3*k)^k*binomial(n-3*k, k));
Formula
a(n) = Sum_{k=0..floor(n/4)} (n-3*k)^k * binomial(n-3*k,k).