A381875 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^2, where C(x) is the g.f. of A000108.
1, 3, 13, 66, 368, 2185, 13570, 87147, 574241, 3861286, 26390591, 182798850, 1280387583, 9053335674, 64534088960, 463249047099, 3345832486407, 24296575830677, 177286818019264, 1299208549351640, 9557974679439901, 70563100013789595, 522608148884843970
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(3*n-3*k+1, n-k)/(n+k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(3*n-3*k+1,n-k)/(n+k+1).
a(n) = binomial(1 + 3*n, n)*hypergeom([-1/2-n, -n, 1+n], [-1/3-n, 1/3-n], 2^2/3^3)/(1 + n). - Stefano Spezia, Mar 09 2025