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URL: https://oeis.org/A001807

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A001807
a(n) = n! * binomial(n,5).
4
120, 4320, 105840, 2257920, 45722880, 914457600, 18441561600, 379369267200, 8014175769600, 174530938982400, 3926946127104000, 91390746230784000, 2200993805058048000, 54855537910677504000, 1414489227553898496000, 37719712734770626560000
OFFSET
5,1
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
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].
FORMULA
E.g.f.: x^5/(1-x)^6. - Geoffrey Critzer, Aug 19 2012
From Amiram Eldar, Sep 18 2025: (Start)
a(n) = A000142(n) * A000389(n).
a(n) ~ sqrt(Pi/2) * n^(n+11/2) / (60 * exp(n)).
Sum_{n>=5} 1/a(n) = 35/48 + 5*e/4 + 25*(gamma-Ei(1))/8, where e = A001113, gamma = A001620, and Ei(1) = A091725.
Sum_{n>=5} (-1)^(n+1)/a(n) = -3625/144 - 155/(6*e) + 1045*(gamma-Ei(-1))/24, where Ei(-1) = -A099285. (End)
MAPLE
G(x):=x^5/(1-x)^6: 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=5..18); # Zerinvary Lajos, Apr 01 2009
MATHEMATICA
Table[n! Binomial[n, 5], {n, 5, 20}] (* T. D. Noe, Aug 10 2012 *)
PROG
(SageMath) [binomial(n, 5)*factorial (n) for n in range(5, 19)] # Zerinvary Lajos, Jul 07 2009
(PARI) for(n=5, 35, print1(n!*binomial(n, 5), ", ")) \\ G. C. Greubel, May 17 2018
(Magma) [Factorial(n)*Binomial(n, 5): n in [5..35]]; // G. C. Greubel, May 17 2018
CROSSREFS
Essentially a column of triangle A021012.
Sequence in context: A179060 A342073 A055360 * A111155 A283344 A223754
KEYWORD
nonn,easy
EXTENSIONS
More terms from Ralf Stephan, Jan 09 2004
STATUS
approved