A371578 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x) )^2.

1, 2, 13, 102, 916, 8880, 90607, 958794, 10426089, 115798342, 1308035135, 14980661482, 173553196140, 2030265152576, 23948922940698, 284543368174220, 3402103050539715, 40903437537402792, 494215527894112099, 5997782678374854902, 73078635875447981850

Offset: 0

Author

Seiichi Manyama, Mar 28 2024

Keywords

• nonn

Crossrefs

Cf. A001629, A052705, A371576, A371577.

Cf. A365184, A371580.

Programs

PARI

a(n, r=2, s=1, t=5, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Formula

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

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A365184.