OFFSET
1,5
LINKS
Robert Israel, Table of n, a(n) for n = 1..477
FORMULA
E.g.f.: 2*arctan(1+x) - Pi/2.
a(n) = n!*(Sum_{i=1..floor(n+1)/2} ((-1)^(n+i)*binomial(n-1, 2*i-2))/(2*i-1))/2^(n-1).
E.g.f. is the series reversion of sec(x) + tan(x) - 1.
From Robert Israel, Jan 17 2017: (Start)
a(n) = (n-1)*a(n-1) - (n-1)*(n-2)*a(n-2)/2.
a(n) = 2^(1-n/2)*(n-1)!*sin(3*Pi*n/4). (End)
MAPLE
seq(2^(1-n/2)*sin(3/4*Pi*n)*(n-1)!, n=1..50); # Robert Israel, Jan 17 2017
MATHEMATICA
Table[2^(1 - n/2)*(n - 1)!*Sin[3*Pi*n/4], {n, 30}] (* Wesley Ivan Hurt, Oct 14 2023 *)
PROG
(Maxima)
a(n):=n!*sum(((-1)^(n+i)*binomial(n-1, 2*i-2))/(2*i-1), i, 1, (n+1)/2)/2^(n-1);
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Mar 17 2013
STATUS
approved