A366238 G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^4*A(x)^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

Links

Table of n, a(n) for n=0..22.

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

Cf. A073157, A366236, A366237.

Cf. A000108.

Sequence in context: A153557 A231103 A114204 * A357402 A129277 A120916

Adjacent sequences: A366235 A366236 A366237 * A366239 A366240 A366241

Keyword

nonn

Author

Seiichi Manyama, Oct 05 2023

Status

approved