A052736 E.g.f. [1 -3x -sqrt(1-6x+x^2) -x*(1-x-sqrt(1-6x+x^2)) ]/2.

0, 0, 2, 24, 384, 8160, 218880, 7116480, 272240640, 11985200640, 596981145600, 33195609216000, 2038500521164800, 137021183973273600, 10006412139653529600, 788930789450259456000, 66790064645111808000000, 6042970648669883056128000, 581917311773908793819136000, 59423732260666221275283456000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 692

Formula

D-finite with recurrence: a(1)=0; a(2)=2; a(3)=24; (-n^3-n^2+4*n+4)*a(n) +(-6+7*n^2+11*n)*a(n+1) +(-7*n-10)*a(n+2) +a(n+3) =0.

a(n) ~ (2-sqrt(2))*sqrt(3*sqrt(2)-4)*n^(n-1)*(3+2*sqrt(2))^n/exp(n). - Vaclav Kotesovec, Oct 05 2013

Conjecture: a(n) = n!*A006319(n-1). - R. J. Mathar, Oct 16 2013

Maple

spec := [S, {B=Prod(Z, C), S=Prod(C, C), C=Union(B, S, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); # end of program
0, seq(simplify( n!*(n-1)*hypergeom([n, 2-n], [3], -1) ), n=1..20);  # Mark van Hoeij, May 29 2013

Mathematica

CoefficientList[Series[1/2-3/2*x-1/2*(1-6*x+x^2)^(1/2)-(1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 05 2013 *)

Prog

(PARI) x='x+O('x^66); concat([0, 0], Vec( serlaplace( 1/2-3/2*x -1/2*(1-6*x+x^2)^(1/2) -(1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x))) \\ Joerg Arndt, May 29 2013

Crossrefs

Sequence in context: A081685 A288944 A052670 * A103904 A219431 A214688

Adjacent sequences: A052733 A052734 A052735 * A052737 A052738 A052739

Keyword

easy,nonn

Author

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

Status

approved