A133132 Number of surjections from an n-element set to a ten-element set.

3628800, 199584000, 6187104000, 142702560000, 2731586457600, 45950224320000, 703098107712000, 10009442963520000, 134672620008326400, 1732015476199008000, 21473732319740064000, 258323865658578720000

Offset: 10

Author

Mohamed Bouhamida, Dec 16 2007

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 10..1000
• Index entries for linear recurrences with constant coefficients, signature (55,-1320,18150,-157773,902055,-3416930,8409500,-12753576,10628640,-3628800).

Crossrefs

Column k=10 of A131689.

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

Programs

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

Mathematica

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

PARI

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

Formula

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.

a(n) = A049435(n) * 10!. - Max Alekseyev, Nov 13 2009

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

E.g.f.: (exp(x)-1)^10. - Alois P. Heinz, May 17 2016

Extensions

More terms from Max Alekseyev, Nov 13 2009

Formula corrected by Charles R Greathouse IV, Mar 07 2010