A369688 G.f. satisfies A(x) = 1 + x*A(x) + x^2*(1-x)^3*A(x)^5.
1, 1, 2, 4, 12, 36, 126, 442, 1644, 6172, 23801, 92731, 366688, 1462852, 5891808, 23898576, 97600556, 400844140, 1654818768, 6862550360, 28576414261, 119434041561, 500849380048, 2106740001442, 8886482895068, 37580609774876, 159303913630686
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, binomial(n, 2*k)*binomial(5*k, k)/(4*k+1));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * binomial(5*k,k) / (4*k+1).