A346058 Expansion of e.g.f. Product_{k>=1} exp(1 - exp(x^k/k!)).

1, -1, -1, 3, 4, 2, -69, -185, 596, 1482, 22051, -8341, -450570, -1503596, -23829233, 144974757, 150086353, 4859956733, 51013196234, -504522222442, 2572161050316, -58533039862692, 69278113622988, 342581575176372, -25348876024693055, 661312712021911319

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..537

Formula

E.g.f.: exp( Sum_{k>=1} (1 - exp(x^k/k!)) ).

E.g.f.: exp( -Sum_{k>=1} A038041(k)*x^k/k! ).

a(n) = -(n-1)! * Sum_{k=1..n} k * (Sum_{d|k} 1/(d! * (k/d)!^d)) * a(n-k)/(n-k)! for n > 0.

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(1-exp(x^k/k!)))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, 1-exp(x^k/k!)))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, sumdiv(k, d, 1/(d!*(k/d)!^d))*x^k))))
(PARI) a(n) = if(n==0, 1, -(n-1)!*sum(k=1, n, k*sumdiv(k, d, 1/(d!*(k/d)!^d))*a(n-k)/(n-k)!));

Crossrefs

Cf. A000587, A038041, A330199, A346056, A346057.

Sequence in context: A210488 A244364 A218610 * A260958 A260965 A278214

Adjacent sequences: A346055 A346056 A346057 * A346059 A346060 A346061

Keyword

sign

Author

Seiichi Manyama, Jul 02 2021

Status

approved