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%I #21 May 31 2022 11:07:50
%S 1,1,2,6,24,240,720,5040,40320,362880,3628800,39916800,479001600,
%T 6227020800,87178291200,1307674368000,20922789888000,355687428096000,
%U 6402373705728000,121645100408832000,2432902008176640000
%N Expansion of e.g.f. (1+x^5-x^6)/(1-x).
%H Vincenzo Librandi, <a href="/A052699/b052699.txt">Table of n, a(n) for n = 0..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=649">Encyclopedia of Combinatorial Structures 649</a>
%F E.g.f.: (1+x^5-x^6)/(1-x).
%F a(n+1) = (n+1)*a(n), for n > 5.
%F a(n) = n! + 5!*[n=5].
%p spec := [S,{S=Union(Sequence(Z),Prod(Z,Z,Z,Z,Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[(1+x^5-x^6)/(1-x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Feb 04 2014 *)
%t Table[n! + 5!*Boole[n==5], {n, 0, 40}] (* _G. C. Greubel_, May 31 2022 *)
%o (SageMath) [factorial(n) + factorial(5)*bool(n==5) for n in (0..30)] # _G. C. Greubel_, May 31 2022
%Y Cf. A000142.
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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