A369483 Expansion of (1/x) * Series_Reversion( x / (1+x+x^3)^2 ).
1, 2, 5, 16, 60, 242, 1014, 4370, 19278, 86678, 395751, 1829742, 8549100, 40302810, 191469165, 915751966, 4405727502, 21307102900, 103526683797, 505118705078, 2473833623696, 12157124607612, 59929746189165, 296271556144028, 1468494529164194, 7296261411708962
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^3)^2)/x) -
PARI
a(n, s=3, t=2, u=0) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(2*n-k+2,n-3*k).