A052661 E.g.f. (2-3x)/((1-x)(1-x-x^2)).

2, 1, 4, 12, 72, 480, 4320, 45360, 564480, 7983360, 127008000, 2235340800, 43110144000, 902918016000, 20399720140800, 494300911104000, 12783824621568000, 351419178958848000, 10230993181753344000

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..417

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 608

Formula

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

Recurrence: {a(1)=1, a(2)=4, a(0)=2, (n^3+6*n^2+11*n+6)*a(n)+(-2*n-6)*a(n+2)+a(n+3)=0}

(1+Sum(1/5*(-1+3*_alpha)*_alpha^(-1-n), _alpha =RootOf(-1+_Z+_Z^2)))*n!

a(n) = n!*A001611(n-1), n>0. - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(2-3x)/((1-x)(1-x-x^2)), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 25 2023 *)

Crossrefs

Sequence in context: A064297 A358501 A323493 * A225117 A088624 A309878

Adjacent sequences: A052658 A052659 A052660 * A052662 A052663 A052664

Keyword

easy,nonn

Author

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

Status

approved