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

0,3

Links

Table of n, a(n) for n=0..21.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 538

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

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 *)

Crossrefs

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

Sequence in context: A271961 A362798 A239836 * A358065 A052586 A052554

Adjacent sequences: A052590 A052591 A052592 * A052594 A052595 A052596

Keyword

easy,nonn

Author

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

Status

approved