A237993 a(n) = |Stirling1(3*n,n)|.

1, 2, 274, 118124, 105258076, 159721605680, 369012649234384, 1206647803780373360, 5304713715525445812976, 30180059720580991603896800, 215760462268683520394805979744, 1893448925578239663637174767335168, 20012008248418194052035539503977759232

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

a(n) ~ n^(2*n) * c^(3*n) * 3^(5*n) / (sqrt(6*Pi*(c-1)*n) * exp(2*n) * (3*c-1)^(2*n)), where c = -LambertW(-1,-exp(-1/3)/3) = 2.237147027773716818...

From Seiichi Manyama, May 20 2025: (Start)

a(n) = A132393(3*n,n).

a(n) = (3*n)! * [x^(3*n)] (-log(1 - x))^n / n!. (End)

Maple

seq(abs(Stirling1(3*n, n)), n=0..20);

Mathematica

Table[Abs[StirlingS1[3*n, n]], {n, 0, 20}]

Crossrefs

Cf. A132393, A187646, A242676, A217913.

Sequence in context: A048534 A135696 A008775 * A174710 A200168 A215043

Adjacent sequences: A237990 A237991 A237992 * A237994 A237995 A237996

Keyword

nonn,easy

Author

Vaclav Kotesovec, May 20 2014

Status

approved