A003704 - OEIS

%I M2867 #28 Feb 16 2015 09:40:36

%S 0,1,-1,3,-10,45,-256,1743,-13840,125625,-1282816,14554683,-181649920,

%T 2473184805,-36478744576,579439207623,-9861412096000,179018972217585,

%U -3452931391553536,70518070842040563,-1520176422094766080

%N Expansion of log(1+sinh(x)).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A003704/b003704.txt">Table of n, a(n) for n = 0..200</a>

%F 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]

%F a(n) ~ (-1)^(n+1) * (n-1)! / (log(1+sqrt(2)))^n. - _Vaclav Kotesovec_, Feb 16 2015

%t With[{nn = 201}, CoefficientList[Series[Log[1 + Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Apr 11 2014 *)

%o (Maxima)

%o 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 */

%Y Cf. A009344, A024293, A080795.

%K sign

%O 0,4

%A _R. H. Hardin_, _Simon Plouffe_

%E Mathematica code replaced by _Vincenzo Librandi_, Apr 11 2014