A052604 E.g.f. (1-x)/(1-2x-x^3+x^4).

1, 1, 4, 30, 240, 2520, 32400, 478800, 8104320, 154586880, 3273177600, 76241088000, 1937561472000, 53340660172800, 1581414202368000, 50234310846720000, 1702089880178688000, 61276407362666496000

Offset

0,3

Links

Table of n, a(n) for n=0..17.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 549

Formula

E.g.f.: -(-1+x)/(1-2*x-x^3+x^4)

Recurrence: {a(1)=1, a(0)=1, a(2)=4, (n^4+35*n^2+50*n+24+10*n^3)*a(n)+(-n^3-9*n^2-26*n-24)*a(n+1)+(-2*n-8)*a(n+3)+a(n+4)=0, a(3)=30}

Sum(-1/643*(-94-127*_alpha-22*_alpha^2+75*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-_Z^3+_Z^4))*n!

a(n)= n!*A052540(n). - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(1-x)/(1-2x-x^3+x^4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 02 2015 *)

Crossrefs

Sequence in context: A346579 A300159 A213102 * A357204 A038225 A086452

Adjacent sequences: A052601 A052602 A052603 * A052605 A052606 A052607

Keyword

easy,nonn

Author

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

Status

approved