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A003720
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E.g.f. tan(tan(tan(x))).
(Formerly M4301)
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0
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1, 6, 168, 10672, 1198080, 208521728, 51874413568, 17449541107712, 7622674735988736, 4193561606973095936, 2836052065377836597248, 2312174256451088534208512, 2236165580390456719589769216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vladimir Kruchinin, Compositae and their properties, arXiv:1103.2582
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FORMULA
| a(n)=b(2*n-1) where b(n)=sum(m=1..n, (((-1)^(m-1)+1)*(sum(j=1..m, j!*2^(m-j-1)*(-1)^((m+1)/2+j)*stirling2(m,j)))*sum(k=m..n,(((-1)^(k-m)+1)*(sum(j=m..k, binomial(j-1,m-1)*j!*2^(k-j-1)*stirling2(k,j)*(-1)^((m+k)/2+j)))*((-1)^(n-k)+1)*sum(j=k,n, binomial(j-1,k-1)*j!*2^(n-j-1)*(-1)^((n+k)/2+j)*stirling2(n,j)))/k!))/m!); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 23 2011]
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MATHEMATICA
| Rest@ Union[ Range[0, 25]! CoefficientList[ Series[Tan@ Tan@ Tan@ x, {x, 0, 25}], x]] (* Robert G. Wilson v *)
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PROG
| (Maxima)
a(n):=b(2*n-1);
b(n):=sum((((-1)^(m-1)+1)*(sum(j!*2^(m-j-1)*(-1)^((m+1)/2+j)*stirling2(m, j), j, 1, m))*sum((((-1)^(k-m)+1)*(sum(binomial(j-1, m-1)*j!*2^(k-j-1)*stirling2(k, j)*(-1)^((m+k)/2+j), j, m, k))*((-1)^(n-k)+1)*sum(binomial(j-1, k-1)*j!*2^(n-j-1)*(-1)^((n+k)/2+j)*stirling2(n, j), j, k, n))/k!, k, m, n))/m!, m, 1, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 23 2011]
(Pari) x='x+O('x^66); /* that many terms */
serlaplace(tan(tan(tan(x)))) /* show terms */ /* Joerg Arndt, Apr 26 2011 */
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CROSSREFS
| Sequence in context: A104729 A106661 A181013 * A002884 A198176 A166762
Adjacent sequences: A003717 A003718 A003719 * A003721 A003722 A003723
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KEYWORD
| nonn
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended and formatted Mar 15 1997 by Olivier Gerard
Corrected definition, Joerg Arndt, Apr 26 2011.
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