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%I #23 May 09 2023 12:27:45
%S 1,1,2,6,48,360,2880,25200,282240,3628800,50803200,758419200,
%T 12454041600,224172748800,4358914560000,90229531392000,
%U 1987665039360000,46595053080576000,1158829640736768000,30411275102208000000,839351192820940800000,24319288473733693440000
%N E.g.f. 1/(1-x-x^4).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=538">Encyclopedia of Combinatorial Structures 538</a>
%F E.g.f.: -1/(-1+x^4+x).
%F Recurrence: {a(1)=1, a(0)=1, a(3)=6, a(2)=2, (-n^4-35*n^2-50*n-24-10*n^3)*a(n) +(-n-4)*a(n+3) +a(n+4)=0}
%F Sum(1/283*(27+36*_alpha^3+48*_alpha^2+64*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^4+_Z))*n!
%F a(n) = n!*A003269(n+1). - _R. J. Mathar_, Nov 27 2011
%p spec := [S,{S=Sequence(Union(Z,Prod(Z,Z,Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p a:= n-> n! * (Matrix([[1,1,0,0], [0,0,1,0], [0,0,0,1], [1,0,0,0]])^n)[1,1]: seq(a(n), n=0..20); # _Alois P. Heinz_, Jun 01 2009
%t With[{nn=20},CoefficientList[Series[1/(1-x-x^4),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Feb 02 2012 *)
%Y Row sums of A145142. - _Alois P. Heinz_, Jun 01 2009
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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