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%I #22 Jun 01 2022 09:43:51
%S 1,0,0,6,24,0,720,10080,40320,362880,10886400,119750400,958003200,
%T 24908083200,523069747200,6538371840000,125536739328000,
%U 3556874280960000,70426110763008000,1338096104497152000
%N Expansion of e.g.f. 1/(1-x^3-x^4).
%H G. C. Greubel, <a href="/A052697/b052697.txt">Table of n, a(n) for n = 0..430</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=646">Encyclopedia of Combinatorial Structures 646</a>
%F E.g.f.: 1/(1 - x^3 - x^4).
%F D-finite recurrence: a(0)=1, a(1)=0, a(2)=0, a(3)=6, a(n+4) = (24 + 26*n + 9*n^2 + n^3)*a(n+1) + (24 + 50*n + 35*n^2 + 10*n^3 + n^4)*a(n).
%F a(n) = (n!/283) * Sum_{alpha=RootOf(-1 + Z^3 + Z^4)} (- 16 - 73*alpha + 3*alpha^2 + 12*alpha^3)*alpha^(-1-n).
%F a(n) = n!*A017817(n). - _R. J. Mathar_, Nov 27 2011
%p spec := [S,{S=Sequence(Prod(Z,Z,Union(Z,Prod(Z,Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[1/(1-x^3-x^4),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 06 2016 *)
%o (Magma) [Factorial(n)*(&+[Binomial(k,n-3*k): k in [0..Floor(n/3)]]): n in [0..30]]; // _G. C. Greubel_, May 31 2022
%o (SageMath) [factorial(n)*sum(binomial(k, n-3*k) for k in (0..n//3)) for n in (0..30)] # _G. C. Greubel_, May 31 2022
%Y Cf. A000142, A017817.
%K easy,nonn
%O 0,4
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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