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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
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
KEYWORD
nonn,easy
AUTHOR
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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Last modified June 12 20:44 EDT 2024. Contains 373360 sequences. (Running on oeis4.)