A372418 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1-x+x^3)^2 ).
1, 0, 0, 2, 2, 2, 15, 32, 53, 192, 527, 1152, 3327, 9578, 24217, 66528, 190357, 515692, 1421172, 4036034, 11272501, 31489762, 89370575, 253106188, 715642419, 2038291672, 5816775442, 16592350656, 47490009821, 136246784272, 391111252072, 1124779108330
Offset: 0
Keywords
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1-x+x^3)^2)/x) -
PARI
a(n, s=3, t=2, u=2) = 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(2*n+2,k) * binomial(n-2*k-1,n-3*k).