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A037960 a(n) = (n+2)!*n*(3*n+1)/24. 7
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

The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1972.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

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

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

CROSSREFS

Cf. A019538, A001286.

Sequence in context: A153598 A180347 A262183 * A222677 A016163 A153884

Adjacent sequences:  A037957 A037958 A037959 * A037961 A037962 A037963

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Feb 20 2017

STATUS

approved

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Last modified October 19 15:49 EDT 2018. Contains 316365 sequences. (Running on oeis4.)