A053508 a(n) = binomial(n-1,3)*n^(n-4).

0, 0, 0, 1, 20, 360, 6860, 143360, 3306744, 84000000, 2338460520, 70946979840, 2332989862060, 82726831323136, 3148511132812500, 128071114403348480, 5546563698427324720, 254873089955815096320, 12387799656377835411984, 635043840000000000000000

Offset: 1

Author

N. J. A. Sloane, Jan 15 2000

Keywords

• nonn

References

• R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Prop. 5.3.2.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A000169, A053506, A053507, A053509.

Programs

GAP

List([1..25], n-> Binomial(n-1,3)*n^(n-4)); # G. C. Greubel, May 15 2019

Magma

[Binomial(n-1,3)*n^(n-4): n in [1..25]]; // G. C. Greubel, Nov 14 2017

Mathematica

Table[Binomial[n-1,3]n^(n-4),{n,25}] (* Harvey P. Dale, Jun 17 2014 *)
With[{nmax = 25}, CoefficientList[Series[LambertW[-x]^4/4!, {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Nov 14 2017 *)

PARI

vector(25, n, binomial(n-1,3)*n^(n-4)) \\ G. C. Greubel, Jan 18 2017

Sage

[binomial(n-1,3)*n^(n-4) for n in (1..25)] # G. C. Greubel, May 15 2019

Formula

E.g.f.: LambertW(-x)^4/4!. - Vladeta Jovovic, Apr 07 2001