A152690 - OEIS

%I #17 Sep 03 2018 23:05:54

%S 1,2,4,16,304,34864,24918064,125436246064,5056710181206064,

%T 1834938528961266006064,6658608419043265483506006064,

%U 265790273955000365854215115506006064

%N Partial sums of superfactorials (A000178).

%H G. C. Greubel, <a href="/A152690/b152690.txt">Table of n, a(n) for n = 1..44</a>

%F G.f.: W(0)/(2-2*x) , where W(k) = 1 + 1/( 1 - x*(k+1)!/( x*(k+1)! + 1/W(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Aug 19 2013

%F a(n) ~ exp(1/12 - 3*n^2/4) * n^(n^2/2 - 1/12) * (2*Pi)^(n/2) / A, where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Jul 10 2015

%F a(n) = n! * G(n+1) + a(n-1), where G(z) is the Barnes G-function. - _Daniel Suteu_, Jul 23 2016

%t lst={};p0=1;s0=0;Do[p0*=a[n];s0+=p0;AppendTo[lst,s0],{n,0,4!}];lst

%t s = 0; lst = {s}; Do[s += BarnesG[n]; AppendTo[lst, s], {n, 2, 13, 1}]; lst (* _Zerinvary Lajos_, Jul 16 2009 *)

%t Table[Sum[BarnesG[k+1],{k,1,n}],{n,1,15}] (* _Vaclav Kotesovec_, Jul 10 2015 *)

%Y Cf. A152686, A152687, A152688, A152689, A053308, A053309, A053295, A053296.

%K nonn

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Dec 10 2008