A191005 - OEIS

%I #9 Jun 27 2013 09:59:19

%S 1,1,2,9,48,325,2640,24997,270592,3295017,44582400,663532001,

%T 10773295104,189494874413,3589475821568,72849709631805,

%U 1577078610001920,36275031333172945,883457851718762496,22711455593084360761,614582936996534026240

%N E.g.f. cos(x)/(cos(x)-x)

%F 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.

%F 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

%t CoefficientList[Series[Cos[x]/(Cos[x]-x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 27 2013 *)

%o (Maxima)

%o 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);

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, Jun 16 2011