A371537 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3 / (1+x))^2.

1, 2, 11, 90, 845, 8620, 92792, 1037474, 11930952, 140223730, 1676824810, 20336742860, 249554057158, 3092735367966, 38653949888993, 486656046354650, 6166315484899445, 78573243500307870, 1006223574171080479, 12943581721362983708, 167170200918998754129

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A349362, A371538, A371539, A371540, A371541.

Cf. A371523.

Programs

PARI

a(n) = 2*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+2, k)/(6*k+2));

Formula

a(n) = 2 * Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+2,k)/(6*k+2).

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349362.