A053509 a(n) = binomial(n-1,4)*n^(n-5).

0, 0, 0, 0, 1, 30, 735, 17920, 459270, 12600000, 372027810, 11824496640, 403786706895, 14772648450560, 577227041015625, 24013333950627840, 1060372471758165020, 49558656380297379840, 2444960458495625410260, 127008768000000000000000

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, A053508.

Programs

GAP

List([1..25], n-> Binomial(n-1,4)*n^(n-5)) # G. C. Greubel, May 15 2019

Magma

[Binomial(n-1,4)*n^(n-5): n in [1..30]]; // G. C. Greubel, Nov 14 2017

Mathematica

Table[Binomial[n-1,4]*n^(n-5), {n,1,25}] (* G. C. Greubel, Jan 18 2017 *)

PARI

vector(25, n, binomial(n-1,4)*n^(n-5)) \\ G. C. Greubel, Jan 18 2017

Sage

[binomial(n-1,4)*n^(n-5) for n in (1..25)] # G. C. Greubel, May 15 2019

Formula

E.g.f.: -LambertW(-x)^5/5!. - Vladeta Jovovic, Apr 07 2001