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A152690 Partial sums of superfactorials (A000178). 1
1, 2, 4, 16, 304, 34864, 24918064, 125436246064, 5056710181206064, 1834938528961266006064, 6658608419043265483506006064, 265790273955000365854215115506006064 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..12.

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

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 *)

CROSSREFS

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

Sequence in context: A112535 A001146 A114641 * A194457 A001128 A280890

Adjacent sequences:  A152687 A152688 A152689 * A152691 A152692 A152693

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 10 2008

STATUS

approved

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Last modified November 24 00:27 EST 2017. Contains 295164 sequences.