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 A009300 Expansion of exp(x/cos(x)). 1
 1, 1, 1, 4, 13, 56, 301, 1688, 11705, 84160, 698521, 6141312, 59340997, 613282944, 6782462597, 80158806016, 1000434618609, 13267800137728, 184576848771889, 2710082835353600, 41577074746699261, 669033814167273472 (list; graph; refs; listen; history; text; internal format)
 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

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