A368318 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^3)^2) ).
1, 2, 5, 16, 62, 264, 1170, 5310, 24599, 116090, 556569, 2703098, 13268900, 65721840, 328050639, 1648535856, 8333536002, 42348587700, 216211838178, 1108514508608, 5704874555112, 29460504457692, 152612723209700, 792833380805160, 4129639139612133
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+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*(n+1), 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+2,n-3*k).