A052630 E.g.f. 1/(1-4x-x^2).

1, 4, 34, 432, 7320, 155040, 3940560, 116847360, 3959786880, 150965337600, 6394994323200, 297985937356800, 15147464243788800, 834153946904678400, 49469459519031552000, 3143339899991875584000, 213046423884047609856000

Offset

0,2

Links

Table of n, a(n) for n=0..16.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 576

Formula

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

Recurrence: {a(0)=1, a(1)=4, (-2-n^2-3*n)*a(n)+(-4*n-8)*a(n+1)+a(n+2)=0}

Sum(1/10*(2+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+4*_Z+_Z^2))*n!

a(n)=n!*A001076(n+1). - R. J. Mathar, Jun 03 2022

Maple

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

Crossrefs

Sequence in context: A145349 A309170 A338163 * A071213 A052629 A151919

Adjacent sequences: A052627 A052628 A052629 * A052631 A052632 A052633

Keyword

easy,nonn

Author

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

Status

approved