A091535 First column (k=2) of array A091534 ((5,2)-Stirling2).

1, 20, 1120, 123200, 22422400, 6098892800, 2317579264000, 1172695107584000, 762251819929600000, 618948477782835200000, 613996889960572518400000, 730656299053081296896000000, 1027302756468632303435776000000, 1684776520608556977634672640000000

Offset

1,2

Comments

The scaled sequence (2/(3n-1)!!!)*a(n) = (3*n-2)!!! = A007559(n), n>=1.

Links

Table of n, a(n) for n=1..14.

Formula

a(n) = (3*n-1)!/(2!*3^(n-(2-1))*(n-1)!) = ((3*n-1)!/2)/A032031(n-1).

a(n) = A091534(n, 2), n>=1.

E.g.f.: (hypergeom([1/3, 2/3, 1], [], 9*x)-1)/2.

a(n) = 9^n*Gamma(n+1/3)*Gamma(n+2/3)*sqrt(3)/(4*Pi). - Peter Luschny, Sep 17 2014

a(n) ~ (sqrt(3)/2) * (3*n/e)^(2*n). - Amiram Eldar, Sep 01 2025

Maple

a := n -> 9^n*GAMMA(n+1/3)*GAMMA(n+2/3)*sqrt(3)/(4*Pi);
seq(a(n), n=1..16); # Peter Luschny, Sep 17 2014

Mathematica

a[n_] := (3*n-1)!/(2!*3^(n-1)*(n-1)!); Array[a, 15] (* Amiram Eldar, Sep 01 2025 *)

Crossrefs

Third column of array A091752 ((-1, 2)-Stirling2).

Cf. A007559, A032031, A091534.

Sequence in context: A177596 A210835 A002305 * A265654 A152130 A151625

Adjacent sequences: A091532 A091533 A091534 * A091536 A091537 A091538

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 23 2004

Status

approved