A052671 Expansion of e.g.f. x^3*(1-x)/(1-2*x).

0, 0, 0, 6, 24, 240, 2880, 40320, 645120, 11612160, 232243200, 5109350400, 122624409600, 3188234649600, 89270570188800, 2678117105664000, 85699747381248000, 2913791410962432000, 104896490794647552000

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..350

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 619

Formula

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

Recurrence: a(0)=0, a(1)=0, a(2)=0, a(3)=6, a(4)=24, a(n) = 2*n*a(n-1).

a(n) = 2^(n-4)*n!, n>3.

G.f.: 6*x^3 + 24*x^4*Hypergeometric2F0([5,1], [], 2*x). - G. C. Greubel, Jun 13 2022

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[x^3(-1+x)/(-1+2x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 13 2014 *)

Prog

(Magma) [0, 0, 0, 6] cat [2^(n-4)*Factorial(n): n in [4..30]]; // G. C. Greubel, Jun 13 2022
(SageMath) [(2^(n-4) - 2^(n-4)*bool(n<3) + (1/2)*bool(n==3))*factorial(n) for n in (0..30)] # G. C. Greubel, Jun 13 2022

Crossrefs

Cf. A000079, A000142.

Sequence in context: A223105 A112675 A052583 * A052733 A323449 A010567

Adjacent sequences: A052668 A052669 A052670 * A052672 A052673 A052674

Keyword

easy,nonn

Author

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

Status

approved