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%I #6 Apr 15 2013 11:10:45
%S 0,1,5,31,31,619,619,5779,5779,69341,69341,3051179,3051179,52884569,
%T 52884569,634649863,634649863,43152570067,43152570067,1093376176159,
%U 1093376176159,2623076354557,2623076354557,241599308325943,241599308325943,1604223576455477
%N Numerators of the sequence with g.f. x*B(x)/(1-2*x), where B(x) denotes the "original" Bernoulli numbers.
%C The generating function of the "original" Bernoulli numbers is
%C B(x) = sum_n A164555(n)*x^n/A027642(n). The generating function C(x) = x*B(x)/(1-2*x) defines a sequence
%C c(n) = 0, 1, 5/2, 31/6, 31/3, 619/30,... obeying c(n+1)-2*c(n) = A164555(n)/A027642(n).
%C a(n) is the numerator of c(n).
%t c[n_] := 2*c[n-1] + BernoulliB[n-1]; c[0] = 0; c[1] = 1; c[2] = 5/2; a[n_] := c[n] // Numerator; Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 15 2013 *)
%Y Cf. A172031.
%K nonn,frac
%O 0,3
%A _Paul Curtz_, Jan 23 2010
%E Edited and extended by _R. J. Mathar_, Mar 14 2010
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