%I #26 Mar 16 2024 15:21:12

%S 3628800,199584000,6187104000,142702560000,2731586457600,

%T 45950224320000,703098107712000,10009442963520000,134672620008326400,

%U 1732015476199008000,21473732319740064000,258323865658578720000

%N Number of surjections from an n-element set to a ten-element set.

%H Vincenzo Librandi, <a href="/A133132/b133132.txt">Table of n, a(n) for n = 10..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (55,-1320,18150,-157773,902055,-3416930,8409500,-12753576,10628640,-3628800).

%F a(n) = 10^n-10*9^n+45*8^n-120*7^n+210*6^n-252*5^n+210*4^n-120*3^n+45*2^n-10.

%F a(n) = A049435(n) * 10!. - _Max Alekseyev_, Nov 13 2009

%F G.f.: 3628800*x^10/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)*(10*x-1)). - _Colin Barker_, Oct 25 2012

%F E.g.f.: (exp(x)-1)^10. - _Alois P. Heinz_, May 17 2016

%t With[{nn=30},Drop[CoefficientList[Series[(Exp[x]-1)^10,{x,0,nn}],x] Range[0,nn]!,10]] (* _Harvey P. Dale_, Sep 01 2016 *)

%o (PARI) sum(k=1,10,(-1)^(10-k)*binomial(10,k)*k^n)

%o (Magma) [10^n-10*9^n+45*8^n-120*7^n+210*6^n-252*5^n+210*4^n-120*3^n+45*2^n-10: n in [10..30]]; // _Vincenzo Librandi_, Apr 11 2012

%Y Column k=10 of A131689.

%Y Cf. A000918, A000919, A000920, A001117, A001118, A049435, A135456.

%K nonn,easy

%O 10,1

%A _Mohamed Bouhamida_, Dec 16 2007

%E More terms from _Max Alekseyev_, Nov 13 2009

%E Formula corrected by _Charles R Greathouse IV_, Mar 07 2010