A003704 Expansion of log(1+sinh(x)).
0, 1, -1, 3, -10, 45, -256, 1743, -13840, 125625, -1282816, 14554683, -181649920, 2473184805, -36478744576, 579439207623, -9861412096000, 179018972217585, -3452931391553536, 70518070842040563, -1520176422094766080
Offset: 0
Keywords
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
Programs
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Mathematica
With[{nn = 201}, CoefficientList[Series[Log[1 + Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Apr 11 2014 *) -
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 */
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
Extensions
Mathematica code replaced by Vincenzo Librandi, Apr 11 2014