A001805 a(n) = n! * binomial(n,3).

6, 96, 1200, 14400, 176400, 2257920, 30481920, 435456000, 6586272000, 105380352000, 1780927948800, 31732897996800, 594991837440000, 11716762337280000, 241867451105280000, 5224336943874048000, 117874102296158208000, 2773508289321369600000

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Coefficients of Laguerre polynomials.

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 3..100
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Essentially a column of triangle A021012.

Programs

Magma

[Factorial(n)*Binomial(n,3): n in [3..30]]; // G. C. Greubel, May 17 2018

Maple

G(x):=x^3/(1-x)^4: f[0]:=G(x): for n from 1 to 18 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=3..18); # Zerinvary Lajos, Apr 01 2009

Mathematica

Table[n! Binomial[n,3], {n,3,30}] (* Harvey P. Dale, Feb 23 2011 *)

PARI

for(n=3, 30, print1(n!*binomial(n,3), ", ")) \\ G. C. Greubel, May 17 2018

Formula

E.g.f.: x^3/(1-x)^4. - Geoffrey Critzer, Aug 19 2012

Extensions

More terms from Ralf Stephan, Jan 09 2004