OFFSET
0,3
FORMULA
a(n)=n!*(2*sum(m..1,(n-1)/2, (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))))/(2*m)!)+1), n>0, a(0)=1.
a(n) ~ n! * cos(r)/((1+sin(r))*r^(n+1)), where r = 0.73908513321516... is the root of the equation r = cos(r). - Vaclav Kotesovec, Jun 27 2013
MATHEMATICA
CoefficientList[Series[Cos[x]/(Cos[x]-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)
PROG
(Maxima)
a(n):=n!*(2*sum((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))/(2*m)!, m, 1, (n-1)/2)+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Jun 16 2011
STATUS
approved