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A366238
G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^4*A(x)^2.
2
1, 2, 8, 42, 224, 1281, 7630, 46816, 294008, 1880588, 12209474, 80251889, 532988530, 3571260662, 24112334292, 163887278097, 1120445503036, 7699924478714, 53160597794588, 368549236730128, 2564649436452878, 17907555498455680, 125426544531794332
OFFSET
0,2
FORMULA
G.f.: 2*(1+x) / (1 + sqrt(1-4*x*(1+x)^5)).
a(n) = Sum_{k=0..n} binomial(5*k+1,n-k) * binomial(2*k,k)/(k+1).
PROG
(PARI) a(n) = sum(k=0, n, binomial(5*k+1, n-k)*binomial(2*k, k)/(k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 05 2023
STATUS
approved