A381746 Expansion of exp( Sum_{k>=1} binomial(10*k-1,2*k) * x^k/k ).

1, 36, 2586, 235884, 24284907, 2689924444, 312907382800, 37699275223260, 4663450108073401, 588854988193808392, 75589352418472567340, 9834912295258236849604, 1294095251234713917535805, 171909332777340128148714400, 23024035140764003881788203616

Offset: 0

Author

Seiichi Manyama, Mar 05 2025

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..462

Crossrefs

Cf. A079489, A381744, A381745.

Cf. A118971, A381752.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(10*k-1, 2*k)*x^k/k)))

Formula

G.f. A(x) satisfies A(x^2) = B(x) * B(-x), where B(x) is the g.f. of A118971.

a(n) = Sum_{k=0..2*n} (-1)^k * A118971(k) * A118971(2*n-k).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(10*k-1,2*k) * a(n-k).

G.f.: B(x)^4, where B(x) is the g.f. of A381752.