A381944 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^3, where B(x) is the g.f. of A001764.
1, 4, 16, 89, 655, 5592, 51594, 499159, 4990821, 51140527, 534152690, 5665496618, 60854697427, 660601882734, 7235771990454, 79870211543625, 887569516968685, 9921579561050637, 111487286796322366, 1258604967618419118, 14268057344239960863, 162358119295068686098
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(n+2*k+2, n-k)/(4*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(n+2*k+2,n-k)/(4*k+1).