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 A133132 Number of surjections from an n-element set to a ten-element set. 1
 3628800, 199584000, 6187104000, 142702560000, 2731586457600, 45950224320000, 703098107712000, 10009442963520000, 134672620008326400, 1732015476199008000, 21473732319740064000, 258323865658578720000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 10,1 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). 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 Cf. A000918, A000919, A000920, A001117, A001118, A135456. Sequence in context: A284207 A061603 A153761 * A228913 A179065 A213872 Adjacent sequences:  A133129 A133130 A133131 * A133133 A133134 A133135 KEYWORD nonn,easy AUTHOR Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 16 2007 EXTENSIONS More terms from Max Alekseyev, Nov 13 2009 Formula corrected by Charles R Greathouse IV, Mar 07 2010 STATUS approved

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Last modified October 13 23:25 EDT 2019. Contains 327983 sequences. (Running on oeis4.)