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

Author

R. H. Hardin, Simon Plouffe

Keywords

• sign

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

Crossrefs

Cf. A009344, A024293, A080795.

Programs

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