A370086 Expansion of e.g.f. exp( Sum_{k>=1} (2*k)!/k! * (x/2)^k/k ).

1, 1, 4, 40, 796, 27196, 1437136, 108931264, 11207616400, 1502077491856, 254091983968576, 52922687300496256, 13303823750214614464, 3970706309867394765760, 1387875547214097148600576, 561507863501525383223535616, 260328000140228961840632033536

Offset: 0

Author

Seiichi Manyama, Feb 08 2024

Keywords

• nonn

Crossrefs

Cf. A000680, A370084.

Programs

PARI

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

Formula

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