A381785 G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)^2), where C(x) is the g.f. of A000108.
1, 2, 7, 45, 335, 2731, 23573, 211741, 1958571, 18529392, 178459000, 1743868792, 17246702932, 172302244669, 1736302280083, 17627794322287, 180133941044517, 1851310247393202, 19123511540724822, 198437973436950204, 2067524004169000212, 21620908821378509071
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(2*k+1, n-k)/(4*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(2*k+1,n-k)/(4*k+1).