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A003721
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Expansion of e.g.f. tan(tanh(x)) (odd powers only).
(Formerly M4571)
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6
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1, 0, -8, 112, -128, -109824, 8141824, -353878016, -9666461696, 5151942574080, -825073851170816, 76429076694827008, 2051308253366714368, -2361338488910424047616, 171581865952588387581952
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = Sum_{i=0..(n-1)} ( ( Sum_{j=1..2*i+1} j!*2^(2*i+1-j-1)*(-1)^(i+j+1)*Stirling2(2*i+1,j) ) * Sum_{k=2*i+1..2*n-1} binomial(k-1,2*i)*k!*(-1)^(1+k)*2^(2*n-k-1)*Stirling2(2*n-1,k) )/(2*i+1)!. - Vladimir Kruchinin, Jun 10 2011
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MATHEMATICA
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With[{nn=30}, Take[CoefficientList[Series[Tan[Tanh[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Nov 05 2011 *)
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PROG
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(Maxima)
a(n):=sum(((sum(j!*2^(2*i+1-j-1)*(-1)^(i+j+1)*stirling2(2*i+1, j), j, 1, 2*i+1))*sum(binomial(k-1, 2*i)*k!*(-1)^(1+k)*2^(2*n-k-1)*stirling2(2*n-1, k), k, 2*i+1, 2*n-1))/(2*i+1)!, i, 0, (n-1)); /* Vladimir Kruchinin, Jun 10 2011 */
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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