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A003723
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E.g.f. exp(tanh(x)).
(Formerly M4327)
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6
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1, 1, 1, -1, -7, -3, 97, 275, -2063, -15015, 53409, 968167, -752343, -77000363, -166831871, 7433044411, 43685848289, -843598411471, -9398558916159, 107426835190735, 2116926930779225, -14072980460605907
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OFFSET
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0,5
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COMMENTS
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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(m=1..n, sum(k=m..n, binomial(k-1,m-1)*k!*(-1)^(m+k)*2^(n-k)*Stirling2(n,k))/m!), n>0, a(0)=1. - Vladimir Kruchinin, Jun 28 2011
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MATHEMATICA
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With[{nn = 30}, CoefficientList[Series[Exp[Tanh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Apr 11 2014 *)
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PROG
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(Maxima)
a(n):=if n=0 then 1 else sum(sum(binomial(k-1, m-1)*k!*(-1)^(m+k)*2^(n-k)*stirling2(n, k), k, m, n)/m!, m, 1, n); /* Vladimir Kruchinin, Jun 28 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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