cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A133132 #26 Mar 16 2024 15:21:12
%S A133132 3628800,199584000,6187104000,142702560000,2731586457600,
%T A133132 45950224320000,703098107712000,10009442963520000,134672620008326400,
%U A133132 1732015476199008000,21473732319740064000,258323865658578720000
%N A133132 Number of surjections from an n-element set to a ten-element set.
%H A133132 Vincenzo Librandi, <a href="/A133132/b133132.txt">Table of n, a(n) for n = 10..1000</a>
%H A133132 <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 A133132 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 A133132 a(n) = A049435(n) * 10!. - _Max Alekseyev_, Nov 13 2009
%F A133132 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 A133132 E.g.f.: (exp(x)-1)^10. - _Alois P. Heinz_, May 17 2016
%t A133132 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 A133132 (PARI) sum(k=1,10,(-1)^(10-k)*binomial(10,k)*k^n)
%o A133132 (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 A133132 Column k=10 of A131689.
%Y A133132 Cf. A000918, A000919, A000920, A001117, A001118, A049435, A135456.
%K A133132 nonn,easy
%O A133132 10,1
%A A133132 _Mohamed Bouhamida_, Dec 16 2007
%E A133132 More terms from _Max Alekseyev_, Nov 13 2009
%E A133132 Formula corrected by _Charles R Greathouse IV_, Mar 07 2010