A391200 Expansion of g^2/(1 - x*g^2)^3, where g = 1+x*g^4 is the g.f. of A002293.

1, 5, 27, 164, 1089, 7704, 57047, 437002, 3435777, 27571378, 224936412, 1860175548, 15558737618, 131392930851, 1118807344341, 9595095725794, 82807004376509, 718603486951077, 6266854365373174, 54893800225251404, 482746705857692856, 4260629554985325028

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

Prog

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

Crossrefs

Cf. A390713, A391199.

Cf. A002057, A002293.

Sequence in context: A081924 A366176 A368317 * A138772 A258789 A367259

Adjacent sequences: A391197 A391198 A391199 * A391201 A391202 A391203

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2025

Status

approved