A158615 Expansion of Sum_{n>0} n*n!*x^n/(1-n!*x^n).

1, 5, 19, 105, 601, 4445, 35281, 324897, 3266569, 36360065, 439084801, 5751188913, 80951270401, 1220673888257, 19615124183329, 334777645154817, 6046686277632001, 115243914079782593, 2311256907767808001

Offset: 1

Author

Vladeta Jovovic, Mar 22 2009

Keywords

• easy
• nonn

Comments

a(n) = Sum_{d|n} d*d!^(n/d).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..440

Crossrefs

Cf. A077365, A265950.

Programs

Maple

nmax := 40: gf := add( taylor( n*n!*x^n/(1-n!*x^n),x=0,nmax+1),n=1..nmax ) : coeffs(convert(gf,polynom)) ; # R. J. Mathar, Mar 30 2009

Mathematica

nmax=20; Rest[CoefficientList[Series[Sum[k*k!*x^k/(1-k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 19 2015 *)

Formula

a(n) ~ n * n!. - Vaclav Kotesovec, Dec 19 2015

Extensions

More terms from R. J. Mathar, Mar 30 2009