A381867 G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x)^2, where C(x) is the g.f. of A000108.
1, 3, 10, 44, 239, 1464, 9610, 65946, 466951, 3385259, 24999475, 187385168, 1421901090, 10901237530, 84312106160, 657031204068, 5153954345309, 40663760712441, 322478148002872, 2569086552458460, 20551321340065924, 165009872444132477, 1329352163579556971, 10742386009423170696
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(3*k+1, k)*binomial(n+k+1, n-k)/(3*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(3*k+1,k) * binomial(n+k+1,n-k)/(3*k+1).
a(n) = (1 + n)*hypergeom([1/3, 2/3, -n, 2+n], [1, 3/2, 3/2], -3^3/2^4). - Stefano Spezia, Mar 09 2025