A052681 Expansion of e.g.f. (1-x)/(1 - x - x^2 - 2*x^3 + 2*x^4).

1, 0, 2, 18, 48, 840, 9360, 90720, 1653120, 25764480, 442713600, 9540115200, 201659673600, 4744989849600, 123531638630400, 3325415917824000, 97123590660096000, 3021564701675520000, 98526128957448192000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 629

Formula

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

Recurrence: a(0)=1, a(1)=0, a(2)=2, a(3)=18, a(n+4) = (n+4)*a(n+3) + (12 + 7*n + n^2)*a(n+2) + (48 + 52*n + 18*n^2 + 2*n^3)*a(n+1) - 2*(n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*a(n).

a(n) = (n!/353)*Sum_{alpha=RootOf(1 - Z - z^2 - 2*Z^3 + 2*Z^4)} (18 + 106*alpha - 33*alpha^2 - 28*alpha^3)*alpha^(-1-n).

a(n) = n!*A052546(n). - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(1-x)/(1-x-x^2-2x^3+2x^4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 23 2014 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( (1-x)/(1-x-x^2-2*x^3+2*x^4) ))); // G. C. Greubel, Jun 09 2022
(SageMath)
def A052681_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( (1-x)/(1-x-x^2-2*x^3+2*x^4) ).egf_to_ogf().list()
A052681_list(40) # G. C. Greubel, Jun 09 2022

Crossrefs

Cf. A000142, A052546.

Sequence in context: A304933 A126909 A139268 * A208652 A223469 A048910

Adjacent sequences: A052678 A052679 A052680 * A052682 A052683 A052684

Keyword

easy,nonn

Author

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

Status

approved