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A037960 a(n) = n*(3*n+1)*(n+2)!/24. 8
0, 1, 14, 150, 1560, 16800, 191520, 2328480, 30240000, 419126400, 6187104000, 97037740800, 1612798387200, 28332944640000, 524813313024000, 10226013557760000, 209144207720448000, 4480594531725312000, 100357207837286400000, 2345925761384325120000, 57136703662028390400000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
For n>=1, a(n) is equal to the number of surjections from {1,2,..,n+2} onto {1,2,...,n}. - Aleksandar M. Janjic and Milan Janjic, Feb 24 2007
REFERENCES
Identity (1.18) in H. W. Gould, Combinatorial Identities, Morgantown, 1972; page 3.
LINKS
H. W. Gould, ed. J. Quaintance, Combinatorial Identities, May 2010 (identity 10.3, p.45)
FORMULA
a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*j^(n+2). - Vladimir Kruchinin, Jun 01 2013
(3*n-2)*(n-1)*a(n) - n*(n+2)*(3*n+1)*a(n-1) = 0. - R. J. Mathar, Jul 26 2015
E.g.f.: x*(1 + 2*x)/(1 - x)^5. - Ilya Gutkovskiy, Feb 20 2017
From G. C. Greubel, Jun 20 2022: (Start)
a(n) = n!*StirlingS2(n+2, n).
a(n) = A131689(n+2, n).
a(n) = A019538(n+2, n). (End)
MATHEMATICA
Table[(n+2)!*n*(3n+1)/24, {n, 0, 20}] (* Harvey P. Dale, Oct 16 2014 *)
PROG
(PARI) n*(3*n+1)*(n+2)!/24 \\ Charles R Greathouse IV, Nov 02 2011
(Magma) [Factorial(n+2)*n*(3*n+1)/24: n in [0..25]]; // Vincenzo Librandi, Feb 20 2017
(SageMath) [factorial(n)*stirling_number2(n+2, n) for n in (0..30)] # G. C. Greubel, Jun 20 2022
CROSSREFS
Sequence in context: A180347 A262183 A357484 * A222677 A016163 A153884
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Feb 20 2017
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)