A052633 E.g.f. x^2*(1+x-x^2)/(1-x)^2.

0, 0, 2, 18, 96, 600, 4320, 35280, 322560, 3265920, 36288000, 439084800, 5748019200, 80951270400, 1220496076800, 19615115520000, 334764638208000, 6046686277632000, 115242726703104000, 2311256907767808000

Offset

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 579

Formula

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

Recurrence: {a(0)=0, a(1)=0, a(2)=2, a(3)=18; for n > 3, a(n) = a(n-1)*n^2/(n-1)}. [Simplified by Jon E. Schoenfield, Aug 11 2017]

For n > 2, a(n) = n*n!.

Maple

spec := [S, {S=Prod(Z, Z, Sequence(Z), Union(Z, Sequence(Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
restart:printlevel := -1; a := [0]; T := x->LambertW(-x); f := series(((1+T(x)))/(1-T(x)), x, 24); for m from 1 to 19 do a := [op(a), op(2*m, f)*m! ] od; print(a); # Zerinvary Lajos, Mar 28 2009

Mathematica

With[{nn=20}, CoefficientList[Series[x^2 (1+x-x^2)/(1-x)^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 27 2016 *)

Crossrefs

Essentially the same as A001563.

Sequence in context: A157052 A280157 A224616 * A052638 A127553 A055357

Adjacent sequences: A052630 A052631 A052632 * A052634 A052635 A052636

Keyword

easy,nonn

Author

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

Status

approved