A381780 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * C(x*A(x)^3), where C(x) is the g.f. of A000108.
1, 2, 13, 122, 1348, 16317, 209366, 2797461, 38509302, 542367569, 7778173646, 113196865436, 1667497600735, 24816081138489, 372551391235504, 5635157636123317, 85797446797707896, 1313857342649814042, 20222887980813290849, 312694810135597988049, 4854881337618505385339
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(2*n+k+1, n-k)/(2*n+3*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(2*n+3*k+1,k) * binomial(2*n+k+1,n-k)/(2*n+3*k+1).