OFFSET
0,4
FORMULA
a(2*n) = A001791(n).
a(2*n+1) = A000917(n-1).
a(n) = n^(n mod 2)*binomial(2*floor(n/2), floor(n/2)-1).
a(n) = A162246(n, n+2) = n!/((n-ceiling((n+2)/2))!*floor((n+2)/2)!)) if n > 1, otherwise 0.
a(n) = A056040(n)*floor(n/2)/(floor(n/2)+1).
G.f.: -((p - 1 - x*(p - 1 + 2*x*(2*p - 3 + x*(3 + 4*x - 2*p))))/(2*x^2*p^3)), where p=sqrt(1-4*x^2). - Benedict W. J. Irwin, Aug 15 2016
MATHEMATICA
CoefficientList[Series[-((-1 + Sqrt[1 - 4 x^2] -x (-1 + Sqrt[1 - 4 x^2] +
2 x (-3 + 2 Sqrt[1 - 4 x^2] +x (3 + 4 x - 2 Sqrt[1 - 4 x^2]))))/
(2 x^2 (1 - 4 x^2)^(3/2))), {x, 0, 30}], x] (* Benedict W. J. Irwin, Aug 15 2016 *)
Table[(n! #)/(#! (# + 1)!) &@ Floor[n/2], {n, 0, 34}] (* Michael De Vlieger, Aug 15 2016 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Feb 14 2014
STATUS
approved