A274707 a(n) = A(n) if n is even else a(n) = A(n)*(n-1)/(n+1) with A(n) = ((n-1)!/ floor((n-1)/2)!^2).

0, 1, 1, 6, 4, 30, 15, 140, 56, 630, 210, 2772, 792, 12012, 3003, 51480, 11440, 218790, 43758, 923780, 167960, 3879876, 646646, 16224936, 2496144, 67603900, 9657700, 280816200, 37442160, 1163381400, 145422675, 4808643120, 565722720, 19835652870, 2203961430

Offset

1,4

Links

Table of n, a(n) for n=1..35.

Formula

a(2*n+1) = A001791(n) for n>=0.

a(2*n+2) = A002457(n) for n>=0.

(-1)^(n+1)*a(2*n+1) = A158500(n+1) for n>=1.

G.f.: (2*x^3 + (4*x^2-1)*(2*x^2 -1 + sqrt(1-4*x^2)))/(2*x*(1-4*x^2)^(3/2)). - Benedict W. J. Irwin, Aug 15 2016

D-finite with recurrence: -(n-2)*(n+1)*(n^3-3*n^2-2*n+12)*a(n) -4*n*(n-1)*(2*n-7)*a(n-1) +4*(n-1)*(n-2)*(n^3-5*n+8)*a(n-2)=0. - R. J. Mathar, Oct 07 2016

Maple

a := proc(n) ((n-1)!/iquo(n-1, 2)!^2);
if n::even then % else % * (n-1)/(n+1) fi end:
seq(a(n), n=1..35);

Mathematica

CoefficientList[Series[(2 x^3 + (-1 + 4 x^2) (-1 + 2 x^2 + Sqrt[1 - 4 x^2]))/(2 x (1 - 4 x^2)^(3/2)), {x, 0, 20}], x] (* Benedict W. J. Irwin, Aug 15 2016 *)
Table[If[EvenQ@ n, #, # (n - 1)/(n + 1)] &@((n - 1)!/Floor[(n - 1)/2]!^2), {n, 35}] (* Michael De Vlieger, Aug 15 2016 *)

Crossrefs

Cf. A001791, A002457, A158500.

Sequence in context: A121682 A237425 A191567 * A372524 A354093 A377018

Adjacent sequences: A274704 A274705 A274706 * A274708 A274709 A274710

Keyword

nonn

Author

Peter Luschny, Jul 08 2016

Status

approved