A347005 E.g.f.: Product_{k>=1} 1 / (1 - exp(x) * x^k / k!).

1, 1, 5, 28, 205, 1856, 19964, 249005, 3535613, 56339884, 996009280, 19350090365, 409850078356, 9400728524669, 232154433941057, 6141705628777193, 173295665869432733, 5195039603196754564, 164890990869273983108, 5524278740902526776085, 194815729875439415542760

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

E.g.f.: Product_{k>=1} 1 / (1 - Sum_{j>=k} binomial(j,k) * x^j / j!).

a(n) ~ c * n! / ((1 + LambertW(1)) * LambertW(1)^n), where c = Product_{k>=2} (1/(1 - LambertW(1)^(k-1)/k!)) = 1.487589725380080111479849424209442083... - Vaclav Kotesovec, Aug 10 2021

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1 - Exp[x] x^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A005651, A140585, A265953, A347006.

Sequence in context: A356409 A332711 A292426 * A356025 A367272 A317968

Adjacent sequences: A347002 A347003 A347004 * A347006 A347007 A347008

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 10 2021

Status

approved