%I #19 Nov 14 2016 03:26:52
%S 0,1,1,4,3,33,155,1195,5418,72373,496027,6851051,59706592,986009607,
%T 10430165629,193892831665,2439695949632,50409517110169,
%U 737532991565959,16755308524034767,279581740874221016
%N E.g.f. -log(sech(x) - log(x+1)).
%C The inner function is sech(x) - log(1+x) = 1 - x - x^3/3 + 11*x^4/24 - x^5/5 + 59*x^6/720 - x^7/7 + ... = 1 - x/1! + 0*x^2/2! - 2*x^3/3! + 11*x^4/4! - 24*x^5/5! + 59*x^6/6! - ...
%H G. C. Greubel, <a href="/A013558/b013558.txt">Table of n, a(n) for n = 0..200</a>
%e x + 1/2!*x^2 + 4/3!*x^3 + 3/4!*x^4 + 33/5!*x^5 ...
%t CoefficientList[Series[-Log[Sech[x]-Log[x+1]], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Nov 12 2016 *)
%K nonn
%O 0,4
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Offset and another leading 1 from _R. J. Mathar_, Dec 22 2011
%E a(0)=0 prepended by _Vaclav Kotesovec_, Nov 12 2016