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A003717
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Expansion of sin(tanh(x)).
(Formerly M3143)
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3
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1, -3, 37, -959, 41641, -2693691, 241586893, -28607094455, 4315903789009, -807258131578995, 183184249105857781, -49548882107764546223, 15742588857552887269753, -5802682207845642276301995
(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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FORMULA
| a(n)=(-1)^(n-1)*b(2*n-1), b(n)=sum(k=1..n,(1-(-1)^k)/k!*((-1)^(n-k)+1)* sum(j=k..n, binomial(j-1,k-1)*j!*2^(n-j-2)*(-1)^((n+k)/2+j)* stirling2(n,j))). [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 21 2011]
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MATHEMATICA
| Sin[ Tanh[ x ] ] (* Odd Part *)
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PROG
| (Maxima)
a(n):=(-1)^(n-1)*b(2*n-1);
b(n):=sum((1-(-1)^k)/k!*((-1)^(n-k)+1)*sum(binomial(j-1, k-1)*j!*2^(n-j-2)*(-1)^((n+k)/2+j)*stirling2(n, j), j, k, n), k, 1, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 21 2011]
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CROSSREFS
| Sequence in context: A155667 A143639 A143412 * A201697 A003716 A051396
Adjacent sequences: A003714 A003715 A003716 * A003718 A003719 A003720
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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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