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

%I

%S 0,1,14,150,1560,16800,191520,2328480,30240000,419126400,6187104000,

%T 97037740800,1612798387200,28332944640000,524813313024000,

%U 10226013557760000,209144207720448000,4480594531725312000,100357207837286400000,2345925761384325120000,57136703662028390400000

%N a(n) = (n+2)!*n*(3*n+1)/24.

%C 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

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

%H Vincenzo Librandi, <a href="/A037960/b037960.txt">Table of n, a(n) for n = 0..300</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

%H H. W. Gould, ed. J. Quaintance, <a href="http://www.math.wvu.edu/~gould/Vol.4.PDF">Combinatorial Identities</a>, May 2010 (identity 10.3, p.45)

%F a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*j^(n+2). [_Vladimir Kruchinin_, Jun 01 2013]

%F (3*n-2)*(n-1)*a(n) - n*(n+2)*(3*n+1)*a(n-1) = 0. - _R. J. Mathar_, Jul 26 2015

%F E.g.f.: x*(1 + 2*x)/(1 - x)^5. - _Ilya Gutkovskiy_, Feb 20 2017

%t Table[(n+2)!*n*(3n+1)/24,{n,0,20}] (* _Harvey P. Dale_, Oct 16 2014 *)

%o (PARI) n*(3*n+1)*(n+2)!/24 \\ _Charles R Greathouse IV_, Nov 02 2011

%o (MAGMA) [Factorial(n+2)*n*(3*n+1)/24: n in [0..25]]; // _Vincenzo Librandi_, Feb 20 2017

%Y Cf. A019538, A001286.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Feb 20 2017

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Last modified February 17 18:46 EST 2019. Contains 320222 sequences. (Running on oeis4.)