A365761 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^2*A(x)^5).
1, 1, 1, 2, 8, 29, 91, 289, 1009, 3706, 13606, 49822, 184726, 696052, 2648746, 10132072, 38952970, 150635860, 585724594, 2287631614, 8968247626, 35281363830, 139256375922, 551306272137, 2188516471579, 8709331962133, 34739262293455, 138863195368540
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(n+3*k+1, n-2*k)/(n+3*k+1));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(n+3*k+1,n-2*k) / (n+3*k+1) = Sum_{k=0..floor(n/3)} binomial(n+3*k,6*k) * binomial(6*k,k) / (5*k+1).