A052718 E.g.f. 1 - x - sqrt(1-4*x).

0, 1, 4, 24, 240, 3360, 60480, 1330560, 34594560, 1037836800, 35286451200, 1340885145600, 56317176115200, 2590590101299200, 129529505064960000, 6994593273507840000, 405686409863454720000, 25152557411534192640000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..365

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 674

Formula

a(0)=0, a(1)=1, a(n) = 2^(2n-1) * Gamma(n-1/2) / sqrt(Pi) for n>=2. - Jon E. Schoenfield, Jan 11 2015

D-finite with recurrence: a(1)=1; a(2)=4; (2-4*n)*a(n) + a(n+1) = 0.

O.g.f.: 1-x-_2F_0(-1/2,1;;4*x). - R. J. Mathar, Feb 23 2010

G.f.: 1-x - G(0)/2, where G(k)= 1 + 1/(1 - x*(4*k-2)/(x*(4*k-2) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 04 2013

a(n) = n!*A068875(n-1). - R. J. Mathar, Oct 18 2013

Maple

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

Mathematica

s=2; lst={0, 1}; Do[s+=n*s+s; AppendTo[lst, s], {n, 0, 5!, 4}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 50}, CoefficientList[Series[1 - x - Sqrt[1 - 4*x], {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Feb 16 2017 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(1-x-sqrt(1-4*x)))) \\ G. C. Greubel, Feb 16 2017

Crossrefs

Sequence in context: A346631 A307826 A239840 * A061640 A126391 A006088

Adjacent sequences: A052715 A052716 A052717 * A052719 A052720 A052721

Keyword

easy,nonn

Author

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

Status

approved