A114038 Analog of A113869 for three generators.

1, 0, -1, 0, -3, -6, -38, -186, -1181, -8094, -61865, -516702, -4688020, -45887352, -481954769, -5406249972, -64506680939, -815807306442, -10901200843386, -153475188129114, -2270769144678657, -35226976789341426, -571781884343282417, -9691701188493783546

Offset: 0

Author

N. J. A. Sloane, Feb 01 2006

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400
• John D. Dixon, Asymptotics of Generating the Symmetric and Alternating Groups, Electronic Journal of Combinatorics, Item R56 of Volume 12(1), 2005.

Crossrefs

Related to A113871 in the same way that A113869 is related to A003319.

Programs

Mathematica

nmax=30; A113871 = Rest[CoefficientList[Series[1/Sum[(k!)^2 x^k,{k,0,nmax}],{x,0,nmax}],x]]; Table[SeriesCoefficient[1 + Sum[A113871[[j]]/Product[n-i+1,{i,1,j}]^2,{j,1,nmax}],{n,Infinity,k}],{k,0,nmax}] (* Vaclav Kotesovec, Jul 28 2015 *)

Formula

a(n) ~ -Pi * n^(n+1) / (2^(n+4) * exp(n) * (log(2))^(n+3/2)). - Vaclav Kotesovec, Jul 28 2015

Extensions

Missing a(3)=0 and more terms added by Vaclav Kotesovec, Jul 28 2015