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A003706
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E.g.f. sin(tan(x)), zeros omitted.
(Formerly M3176)
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4
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1, 1, -3, -275, -15015, -968167, -77000363, -7433044411, -843598411471, -107426835190735, -14072980460605907, -1424712499632406371, 164163646840636339593, 237037449673450822122569
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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), b(n)=sum(k=1..n, ((-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))*((-1)^((k+3)/2)-(-1)^((3*k+3)/2))/(2*k!)); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 23 2011]
a(n):=sum(m=0..n, sum(j=0..2*n-2*m, binomial(j+2*m,2*m)*(j+2*m+1)!*2^(2*n-2*m-j)*(-1)^(n+j)* stirling2(2*n+1,j+2*m+1))/((2*m+1)!)); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Jan 21 2012]
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MATHEMATICA
| Sin[ Tan[ x ] ] (* Odd Part *)
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PROG
| (Maxima)
a(n):=b(2*n-1);
b(n):=sum(((-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)*((-1)^((k+3)/2)-(-1)^((3*k+3)/2))/(2*k!), k, 1, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 23 2011]
a(n):=sum(sum(binomial(j+2*m, 2*m)*(j+2*m+1)!*2^(2*n-2*m-j)*(-1)^(n+j)*stirling2(2*n+1, j+2*m+1), j, 0, 2*n-2*m)/((2*m+1)!), m, 0, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Jan 21 2012]
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CROSSREFS
| Sequence in context: A171358 A115477 A051365 * A068250 A096126 A057599
Adjacent sequences: A003703 A003704 A003705 * A003707 A003708 A003709
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KEYWORD
| sign
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Corrected name, Joerg Arndt, Apr 23 2011.
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