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A133132
Number of surjections from an n-element set to a ten-element set.
3
3628800, 199584000, 6187104000, 142702560000, 2731586457600, 45950224320000, 703098107712000, 10009442963520000, 134672620008326400, 1732015476199008000, 21473732319740064000, 258323865658578720000
OFFSET
10,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (55,-1320,18150,-157773,902055,-3416930,8409500,-12753576,10628640,-3628800).
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
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 *)
PROG
(PARI) sum(k=1, 10, (-1)^(10-k)*binomial(10, k)*k^n)
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Dec 16 2007
EXTENSIONS
More terms from Max Alekseyev, Nov 13 2009
Formula corrected by Charles R Greathouse IV, Mar 07 2010
STATUS
approved