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

0,4

Links

Table of n, a(n) for n=0..21.

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

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

Mathematica

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

Prog

(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 */

Crossrefs

Sequence in context: A243549 A344418 A159595 * A192372 A304670 A316117

Adjacent sequences: A009297 A009298 A009299 * A009301 A009302 A009303

Keyword

nonn,easy

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

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

Status

approved