A243802 E.g.f.: exp( Sum_{n>=1} (exp(n*x) - 1)^n / n ).

1, 1, 6, 95, 3043, 167342, 14175447, 1715544861, 280986929888, 59828264507385, 16056622678756319, 5300955907062294008, 2110872493413444115109, 997542435957462115205773, 551887323312314977683048334, 353334615697796170374209624907, 259179558930246734075836153918127

Offset

0,3

Comments

Compare to: exp( Sum_{n>=1} (exp(x) - 1)^n/n ) = 1/(2-exp(x)), the e.g.f. of Fubini numbers (A000670).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Formula

a(n) ~ c * d^n * (n!)^2 / n^(3/2), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491..., r = 0.873702433239668330496568304720719298... is the root of the equation exp(1/r)/r + (1+exp(1/r)) * LambertW(-exp(-1/r)/r) = 0, and c = 0.37498840921734807101035131780130551... . - Vaclav Kotesovec, Aug 21 2014

Example

E.g.f.: A(x) = 1 + x + 6*x^2/2! + 95*x^3/3! + 3043*x^4/4! + 167342*x^5/5! +...

Prog

(PARI) {a(n) = n!*polcoeff( exp( sum(m=1, n+1, (exp(m*x +x*O(x^n)) - 1)^m / m) ), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A244585, A244437.

Sequence in context: A290984 A338788 A326436 * A119627 A336825 A116158

Adjacent sequences: A243799 A243800 A243801 * A243803 A243804 A243805

Keyword

nonn

Author

Paul D. Hanna, Aug 21 2014

Status

approved