A174661 E.g.f.: Product_{n>=1} 1/(1 - x^n/n!)^n.

1, 1, 4, 15, 82, 475, 3456, 26719, 239996, 2313609, 24846640, 285861301, 3586817928, 47988744115, 690525294018, 10547453864445, 171595180564816, 2949836193259105, 53630566660122696, 1025856767305899229, 20638503314068334480

Offset: 0

Author

Paul D. Hanna, Nov 30 2010

Keywords

• nonn

Comments

Compare to the e.g.f. of A032315: Product_{n>=1} (1 + x^n/n!)^n.

Examples

			E.g.f.: A(x) = 1 + x + 4*x^2/2! + 15*x^3/3! + 82*x^4/4! + ...;
A(x) = 1/((1-x)*(1-x^2/2!)^2*(1-x^3/3!)^3*(1-x^4/4!)^4*(1-x^5/5!)^5* ...).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..380

Crossrefs

Cf. variant: A032315.

Programs

PARI

{a(n)=n!*polcoeff(prod(k=1,n,1/(1-x^k/k!+x*O(x^n))^k),n)}

Formula

a(n) ~ c * n!, where c = product_{k>=2} 1/(1-1/k!)^k = 8.6304199482678945455168174204973507297310235756... . - Vaclav Kotesovec, Nov 03 2014

E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} j*x^(j*k)/(k*(j!)^k)). - Ilya Gutkovskiy, Sep 12 2018