A364195 Expansion of g.f. A(x) satisfying A(x) = 1 + x * A(x)^5 * (1 + A(x)^2).

1, 2, 24, 412, 8280, 181904, 4232048, 102479184, 2555884896, 65207430848, 1693785940992, 44643489969792, 1190986788639232, 32097745138518528, 872595854798515456, 23900545715576753408, 658934625866433496576, 18271554709525993556992, 509241947434834351042560

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * binomial(5*n+2*k+1,n)/(5*n+2*k+1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(5*n+2*k+1, n)/(5*n+2*k+1));

Crossrefs

Cf. A217364, A363006, A363305, A364196.

Cf. A349310, A363304, A363311.

Sequence in context: A103904 A219431 A214688 * A003102 A370847 A304318

Adjacent sequences: A364192 A364193 A364194 * A364196 A364197 A364198

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 13 2023

Status

approved