A381783 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * C(x*A(x)), where C(x) is the g.f. of A000108.
1, 2, 11, 79, 645, 5682, 52643, 505575, 4987933, 50250625, 514787110, 5346336739, 56161123273, 595667090038, 6370314162095, 68616488830785, 743733580011957, 8106009997644507, 88783190884441892, 976705067814061730, 10787334777299825522, 119569153425125828365
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(3*n-2*k+1, n-k))/(3*n+1);
Formula
a(n) = (1/(3*n+1)) * Sum_{k=0..n} binomial(3*n+1,k) * binomial(3*n-2*k+1,n-k).