A191005 E.g.f. cos(x)/(cos(x)-x)

1, 1, 2, 9, 48, 325, 2640, 24997, 270592, 3295017, 44582400, 663532001, 10773295104, 189494874413, 3589475821568, 72849709631805, 1577078610001920, 36275031333172945, 883457851718762496, 22711455593084360761, 614582936996534026240

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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

Sequence in context: A052826 A358264 A246759 * A257544 A295944 A356632

Adjacent sequences: A191002 A191003 A191004 * A191006 A191007 A191008

Keyword

nonn

Author

Vladimir Kruchinin, Jun 16 2011

Status

approved