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 A003704 Expansion of log(1+sinh(x)). (Formerly M2867) 13
 0, 1, -1, 3, -10, 45, -256, 1743, -13840, 125625, -1282816, 14554683, -181649920, 2473184805, -36478744576, 579439207623, -9861412096000, 179018972217585, -3452931391553536, 70518070842040563, -1520176422094766080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n) = sum(k=1..n, sum(i=0..k, (-1)^(n+i-1)*(k-2*i)^n * binomial(k,i)) /(k*2^k)). [Vladimir Kruchinin, Apr 20 2011] a(n) ~ (-1)^(n+1) * (n-1)! / (log(1+sqrt(2)))^n. - Vaclav Kotesovec, Feb 16 2015 MATHEMATICA With[{nn = 201}, CoefficientList[Series[Log[1 + Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Apr 11 2014 *) PROG (Maxima) a(n):=sum(sum((-1)^(n+i-1)*(k-2*i)^n*binomial(k, i), i, 0, k)/(k*2^k), k, 1, n); /* Vladimir Kruchinin, Apr 20 2011 */ CROSSREFS Cf. A009344, A024293, A080795. Sequence in context: A020026 A077002 A268224 * A292181 A236409 A348468 Adjacent sequences: A003701 A003702 A003703 * A003705 A003706 A003707 KEYWORD sign AUTHOR R. H. Hardin, Simon Plouffe EXTENSIONS Mathematica code replaced by Vincenzo Librandi, Apr 11 2014 STATUS approved

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Last modified February 21 02:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)