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

0,5

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.

Formula

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

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 *)

Crossrefs

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

Sequence in context: A359968 A025596 A172361 * A000222 A372017 A208649

Adjacent sequences: A114035 A114036 A114037 * A114039 A114040 A114041

Keyword

sign

Author

N. J. A. Sloane, Feb 01 2006

Extensions

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

Status

approved