A052664 E.g.f. (1-x)/(1-2x-3x^2+3x^3).

1, 1, 10, 60, 768, 9480, 161280, 2968560, 65036160, 1568004480, 42507763200, 1259454873600, 40850693452800, 1432712945664000, 54168492771993600, 2193096759549696000, 94738664609132544000, 4347659200973856768000

Offset

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 611

Formula

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

Recurrence: {a(1)=1, a(0)=1, a(2)=10, (3*n^3+18*n^2+33*n+18)*a(n)+(-18-3*n^2-15*n)*a(n+1)+(-2*n-6)*a(n+2)+a(n+3)}

Sum(-1/107*(-13-38*_alpha+33*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-3*_Z^2+3*_Z^3))*n!

a(n) = n!*A052538(n). - R. J. Mathar, Nov 27 2011

Maple

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

Crossrefs

Sequence in context: A004309 A281863 A219368 * A090373 A218427 A354944

Adjacent sequences: A052661 A052662 A052663 * A052665 A052666 A052667

Keyword

easy,nonn

Author

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

Status

approved