A177373 a(n) = 2*n*a(n-1) if the parity of the ratio a(n-1)/a(n-2) is odd, otherwise (for even parity) a(n) = (2n-1)*a(n-1).

1, 2, 6, 36, 252, 2520, 27720, 388080, 5821200, 104781600, 1990850400, 43798708800, 1007370302400, 26191627862400, 707173952284800, 21215218568544000, 657671775624864000, 22360840371245376000, 782629412993588160000, 29739917693756350080000

Offset

0,2

Comments

The sequence is designed to be factorial like in even/ odd 2*n and 2*n-1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = 2*(a(n-1)+(n-1)*(2n-3)*a(n-2)). - R. J. Mathar, Jan 28 2012

E.g.f.: (1+2*x)^(1/4)/(1-2*x)^(3/4). - Vaclav Kotesovec, Oct 21 2012

a(n) ~ n!*2^(n+1/4)/(Gamma(3/4)*n^(1/4)). - Vaclav Kotesovec, Oct 21 2012

Example

The parity of 2/1 = 2 is even, so a(2) = (2*2-1)*2 = 6. The parity of 6/2=3 is odd, so a(3) = (2*3)*6 = 36.

Mathematica

w[ -1] := 1; w[0] := 1;
w[n_] := w[n] = If[Mod[ w[n - 1]/w[n - 2], 2] == 0,
(2* n - 1)*w[n - 1], If[Mod[w[n - 1]/w[n - 2], 2] == 1, 2*n*w[n - 1], 0]] Table[w[n], {n, 0, 20}]
CoefficientList[Series[(1+2*x)^(1/4)/(1-2*x)^(3/4), {x, 0, 20}], x] *Range[0, 20]! (* Vaclav Kotesovec, Oct 21 2012 *)

Crossrefs

Cf. A042948.

Sequence in context: A075096 A347897 A354413 * A109284 A060178 A096939

Adjacent sequences: A177370 A177371 A177372 * A177374 A177375 A177376

Keyword

nonn,easy

Author

Roger L. Bagula, May 07 2010

Status

approved