A369232 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^3)^3 ).
1, 0, 0, 3, 3, 3, 33, 72, 120, 583, 1731, 3888, 13759, 44775, 119793, 381220, 1250328, 3682284, 11455153, 37174428, 114947724, 359381467, 1157319135, 3663615552, 11581104121, 37220909916, 119192219799, 380580143110, 1225279436706, 3948906772872, 12705801908002
Offset: 0
Keywords
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1-x+x^3)^3)/x) -
PARI
a(n, s=3, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u-t+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+3,k) * binomial(n-2*k-1,n-3*k).