A366237 - OEIS

A366237

G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^3*A(x)^2.

1, 2, 7, 33, 161, 843, 4601, 25896, 149254, 876480, 5225616, 31547730, 192470212, 1184804588, 7349888208, 45902094845, 288368474907, 1821096958308, 11554270204142, 73615309821574, 470795634833760, 3021222108762826, 19448517295201332

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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)^4)).

a(n) = Sum_{k=0..n} binomial(4*k+1,n-k) * binomial(2*k,k)/(k+1).

PROG

(PARI) a(n) = sum(k=0, n, binomial(4*k+1, n-k)*binomial(2*k, k)/(k+1));

CROSSREFS

Cf. A073157, A366236, A366238.

Cf. A000108.

Sequence in context: A080119 A162257 A214954 * A369269 A369300 A055724

Adjacent sequences: A366234 A366235 A366236 * A366238 A366239 A366240

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 05 2023

STATUS

approved