A381947 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^3, where B(x) is the g.f. of A002293.
1, 4, 17, 111, 1001, 10507, 118986, 1411789, 17307078, 217422098, 2784080234, 36201950786, 476725871599, 6344524132503, 85198695369123, 1152990558752089, 15708685673520617, 215287198676732925, 2965962577091646604, 41052101428818066604, 570583013508324005560
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(n+2*k+2, n-k)/(5*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(5*k+1,k) * binomial(n+2*k+2,n-k)/(5*k+1).