A052588 Expansion of e..g.f.: (1-x)/(1-x-x^2-x^3+x^4).

1, 0, 2, 12, 48, 600, 5760, 65520, 967680, 14515200, 250387200, 4790016000, 98195328000, 2204365363200, 53178757632000, 1371750412032000, 37828404117504000, 1107254963662848000, 34316723062702080000

Offset

0,3

Links

Table of n, a(n) for n=0..18.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 533

Formula

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

Recurrence: {a(1)=0, a(0)=1, a(2)=2, a(3)=12, (n^4+35*n^2+50*n+24+10*n^3)*a(n) +(-n^3-9*n^2-26*n-24)*a(n+1) +(-n^2-7*n-12)*a(n+2) +(-n-4)*a(n+3) +a(n+4)=0}

Sum(-1/39*(-2-11*_alpha+4*_alpha^2+_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-_Z-_Z^3+_Z^4-_Z^2))*n!

a(n) = n!*A052527(n). - R. J. Mathar

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(1-x)/(1-x-x^2-x^3+x^4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 22 2024 *)

Crossrefs

Sequence in context: A359118 A338522 A277183 * A139239 A060238 A085495

Adjacent sequences: A052585 A052586 A052587 * A052589 A052590 A052591

Keyword

easy,nonn

Author

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

Extensions

Definition clarified by Harvey P. Dale, Jul 22 2024

Status

approved