A052593 E.g.f. 1/(1-x-x^4).

1, 1, 2, 6, 48, 360, 2880, 25200, 282240, 3628800, 50803200, 758419200, 12454041600, 224172748800, 4358914560000, 90229531392000, 1987665039360000, 46595053080576000, 1158829640736768000, 30411275102208000000, 839351192820940800000, 24319288473733693440000

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 538

Crossrefs

Row sums of A145142. - Alois P. Heinz, Jun 01 2009

Programs

Maple

spec := [S,{S=Sequence(Union(Z,Prod(Z,Z,Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
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

Mathematica

With[{nn=20},CoefficientList[Series[1/(1-x-x^4),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 02 2012 *)

Formula

E.g.f.: -1/(-1+x^4+x).

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}

Sum(1/283*(27+36*_alpha^3+48*_alpha^2+64*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^4+_Z))*n!

a(n) = n!*A003269(n+1). - R. J. Mathar, Nov 27 2011