A052610 Expansion of e.g.f. 1/(1-x-2*x^3).

1, 1, 2, 18, 120, 840, 9360, 115920, 1491840, 22861440, 395539200, 7304774400, 148011494400, 3281639961600, 77850214041600, 1975895970048000, 53666956062720000, 1547595999645696000, 47204701332332544000, 1520928690411626496000, 51589687083385651200000, 1836770462015126077440000

Offset

0,3

Links

Table of n, a(n) for n=0..21.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 555.

Formula

Recurrence: a(1)=1, a(0)=1, a(2)=2, (-12*n^2-22*n-12-2*n^3)*a(n) +(-n-3)*a(n+2) +a(n+3)=0.

a(n) = n!*Sum_{alpha in roots(2*z^3+z-1)} (1/29)*(2+6*alpha^2+9*alpha)*alpha^(-1-n).

a(n) = n!*A077949(n). - R. J. Mathar, Jun 03 2022

Maple

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

Mathematica

CoefficientList[Series[1/(1-x-2x^3), {x, 0, 20}], x]*Range[0, 20]! (* Stefano Spezia, Sep 11 2025 *)

Crossrefs

Cf. A077949.

Sequence in context: A007798 A058052 A119578 * A381280 A052653 A342124

Adjacent sequences: A052607 A052608 A052609 * A052611 A052612 A052613

Keyword

easy,nonn

Author

INRIA Encyclopedia of Combinatorial Structures, Jan 25 2000

Extensions

a(19)-a(21) from Stefano Spezia, Sep 11 2025

a(19)-a(21) corrected by Sean A. Irvine, Sep 15 2025

Status

approved