A370471 G.f. satisfies A(x) = 1 + x * A(x)^(1/2) * (1 + A(x)^(5/2)).
1, 2, 7, 36, 215, 1396, 9571, 68174, 499554, 3741430, 28512825, 220388592, 1723616516, 13614340486, 108450776960, 870264507952, 7028286595932, 57081622558906, 465925734601567, 3820141417134780, 31447663707379395, 259821859662976686, 2153756454578830070
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n, k)*binomial(n/2+5*k/2+1, n)/(n/2+5*k/2+1));
Formula
a(n) = Sum{k=0..n} binomial(n,k) * binomial(n/2+5*k/2+1,n)/(n/2+5*k/2+1).