%I #20 Aug 24 2015 12:01:21
%S 1,1,6,76,1620,51780,2310000,136898496,10393064640,982930939200,
%T 113269208976000,15619762139984640,2539231615282602240,
%U 480507998223110457600,104704722014993388288000
%N a(n) is (n+1)!*(n+2)! times coefficient of x^n in (log(1-x))^-1.
%C Related to 'logarithmic numbers'.
%H Philippe Deléham, <a href="/A009763/a009763.pdf">Letter to N. J. A. Sloane, Apr 14 1997</a>
%F log(2*Pi) = 1 + sum{a(n)*(2n+1)/(((n+1)!)^2*n*(n+1)); n>0} = 1.83787706... = A061444. - _Philippe Deléham_, Jan 20 2004
%F Sum_{n>=0} a(n)/((n+1)*(n+1)!*(n+2)!) = Euler constant gamma = 0.5772156649... = A001620. - _Philippe Deléham_, Feb 26 2004
%t Table[(n+2)!*Abs[Sum[StirlingS1[n+1,k]/(k+1),{k,0,n+1}]],{n,0,20}] (* _Vaclav Kotesovec_, Aug 03 2014 *)
%o (PARI) a(n)=local(A); if(n<0,0,n++; A=x/log(1-x+x^2*O(x^n)); n!*(n+1)!*polcoeff(A,n))
%Y a(n)=(n+1)!*(n+2)!*A002206/A002207(n).
%K nonn
%O 0,3
%A _Philippe Deléham_, Apr 14 1997
%E Better description and more terms from Joe Keane (jgk(AT)jgk.org), Aug 13 2002