A158615 - OEIS

%I #9 Dec 19 2015 06:43:50

%S 1,5,19,105,601,4445,35281,324897,3266569,36360065,439084801,

%T 5751188913,80951270401,1220673888257,19615124183329,334777645154817,

%U 6046686277632001,115243914079782593,2311256907767808001

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

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

%H Vaclav Kotesovec, <a href="/A158615/b158615.txt">Table of n, a(n) for n = 1..440</a>

%F a(n) ~ n * n!. - _Vaclav Kotesovec_, Dec 19 2015

%p 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

%t 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 *)

%Y Cf. A077365, A265950.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Mar 22 2009

%E More terms from _R. J. Mathar_, Mar 30 2009