A001805 a(n) = n! * binomial(n,3). (Formerly M4291 N1794)

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

Offset

3,1

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.

Formula

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

From Amiram Eldar, Sep 18 2025: (Start)

a(n) = A000142(n) * A000292(n-2).

a(n) ~ sqrt(Pi/2) * n^(n+7/2) / (3 * exp(n)).

Sum_{n>=3} 1/a(n) = -6 + 3*e + 3*(gamma - Ei(1))/2, where e = A001113, gamma = A001620, and Ei(1) = A091725.

Sum_{n>=3} (-1)^(n+1)/a(n) = -6 - 6/e + 21*(gamma - Ei(-1))/2, where Ei(-1) = -A099285. (End)

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 *)

Prog

(PARI) for(n=3, 30, print1(n!*binomial(n, 3), ", ")) \\ G. C. Greubel, May 17 2018
(Magma) [Factorial(n)*Binomial(n, 3): n in [3..30]]; // G. C. Greubel, May 17 2018

Crossrefs

Essentially a column of triangle A021012.

Cf. A000142, A000292.

Cf. A001113, A001620, A091725, A099285.

Sequence in context: A393582 A202078 A227262 * A387264 A385903 A139743

Adjacent sequences: A001802 A001803 A001804 * A001806 A001807 A001808

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Ralf Stephan, Jan 09 2004

Status

approved