OFFSET
0,4
FORMULA
a(n)=2*n!*sum(m=1..(n-1)/2, ((-1)^(n-1)*sum(j=0..m, binomial((n/2-m+j-1),j)*4^(m-j)*sum(i=0..j, (i-j)^(2*m)*binomial(2*j,i)*(-1)^(m+j-i))))/((n-2*m)*(2*m)!))+(-1)^(n-1)*n!/n. - Vladimir Kruchinin, Jun 16 2011
a(n) ~ (n-1)! * (-1)^(n+1) / r^n, where r = 0.7390851332151606416553120876738734040134117589... (see A003957) is the root of the equation cos(r) = r. - Vaclav Kotesovec, Jan 24 2015
MATHEMATICA
CoefficientList[Series[Log[1 + x*Sec[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)
PROG
(Maxima)
a(n):=2*n!*sum(((-1)^(n-1)*sum(binomial((n/2-m+j-1), j)*4^(m-j)*sum((i-j)^(2*m)*binomial(2*j, i)*(-1)^(m+j-i), i, 0, j), j, 0, m))/((n-2*m)*(2*m)!), m, 1, (n-1)/2)+(-1)^(n-1)*n!/n; /* Vladimir Kruchinin, Jun 16 2011 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved