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Number of surjections from an n-element set to a nine-element set.
3

%I #22 Mar 16 2024 15:21:03

%S 362880,16329600,419126400,8083152000,130456085760,1863435974400,

%T 24359586451200,297846188640000,3457819037312640,38528927611574400,

%U 415357755774998400,4358654246117808000,44733116259693227520

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

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (45,-870,9450,-63273,269325,-723680,1172700,-1026576,362880).

%F a(n) = Sum_{k=1..9} (-1)^(9-k)*binomial(9,k)*k^n.

%F a(n) = A049447(n) * 9!. - _Max Alekseyev_, Nov 12 2009

%F G.f.: -362880*x^9/((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)). - _Colin Barker_, Oct 25 2012

%F E.g.f.: (exp(x) - 1)^9. - _Ilya Gutkovskiy_, Jun 19 2018

%Y Column k=9 of A131689.

%Y Cf. A000918, A000919, A000920, A001117, A001118, A049447, A135456.

%K nonn,easy

%O 9,1

%A _Mohamed Bouhamida_, Dec 21 2007

%E More terms from _Max Alekseyev_, Nov 12 2009