A009300 Expansion of exp(x/cos(x)).

1, 1, 1, 4, 13, 56, 301, 1688, 11705, 84160, 698521, 6141312, 59340997, 613282944, 6782462597, 80158806016, 1000434618609, 13267800137728, 184576848771889, 2710082835353600, 41577074746699261, 669033814167273472

Offset: 0

Author

R. H. Hardin

Keywords

• nonn
• easy

Links

• Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x/Cos[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 10 2015 *)

Maxima

a(n):=sum(binomial(n,k)*(if n=k then 1 else if oddp(n-k) then 0 else sum(sum(binomial(m,j)*2^(1-j)*sum((-1)^((n-k)/2)*binomial(j,i)*(j-2*i)^(n-k),i,0,floor((j-1)/2))*(-1)^(m-j),j,1,m)*(-1)^m*binomial(k+m-1,k-1),m,1,n-k)),k,1,n); /* Vladimir Kruchinin, Sep 12 2010 */

Formula

a(n) = sum(binomial(n,k)*(if n=k then 1 else if oddp(n-k) then 0 else sum(sum(binomial(m,j)*2^(1-j)*sum((-1)^((n-k)/2)*binomial(j,i)*(j-2*i)^(n-k),i,0,floor((j-1)/2))*(-1)^(m-j),j,1,m)*(-1)^m*binomial(k+m-1,k-1),m,1,n-k)),k,1,n), n>0. - Vladimir Kruchinin, Sep 12 2010

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Jul 10 2015