A237993 a(n) = |Stirling1(3*n,n)|.
1, 2, 274, 118124, 105258076, 159721605680, 369012649234384, 1206647803780373360, 5304713715525445812976, 30180059720580991603896800, 215760462268683520394805979744, 1893448925578239663637174767335168, 20012008248418194052035539503977759232
Offset: 0
Programs
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Maple
seq(abs(Stirling1(3*n,n)), n=0..20);
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Mathematica
Table[Abs[StirlingS1[3*n, n]],{n,0,20}]
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)