A152690 Partial sums of superfactorials (A000178).

1, 2, 4, 16, 304, 34864, 24918064, 125436246064, 5056710181206064, 1834938528961266006064, 6658608419043265483506006064, 265790273955000365854215115506006064

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 10 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..44

Crossrefs

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

Programs

Mathematica

lst={};p0=1;s0=0;Do[p0*=a[n];s0+=p0;AppendTo[lst,s0],{n,0,4!}];lst
s = 0; lst = {s}; Do[s += BarnesG[n]; AppendTo[lst, s], {n, 2, 13, 1}]; lst (* Zerinvary Lajos, Jul 16 2009 *)
Table[Sum[BarnesG[k+1],{k,1,n}],{n,1,15}] (* Vaclav Kotesovec, Jul 10 2015 *)

Formula

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

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

a(n) = n! * G(n+1) + a(n-1), where G(z) is the Barnes G-function. - Daniel Suteu, Jul 23 2016