A370249 Coefficient of x^n in the expansion of ( 1/(1-x)^2 * (1+x^3)^2 )^n.
1, 2, 10, 62, 394, 2552, 16810, 112114, 754698, 5116832, 34891260, 239036470, 1644001546, 11344059092, 78497737370, 544507428962, 3785080540682, 26360971309824, 183895618774084, 1284778549054704, 8988079638054044, 62955181189933276, 441442177486335002
Offset: 0
Keywords
Programs
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PARI
a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(3*n-3*k-1,n-3*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^2 / (1+x^3)^2 ). See A369267.