A172030 Numerators of the sequence with g.f. x*B(x)/(1-2*x), where B(x) denotes the "original" Bernoulli numbers.

0, 1, 5, 31, 31, 619, 619, 5779, 5779, 69341, 69341, 3051179, 3051179, 52884569, 52884569, 634649863, 634649863, 43152570067, 43152570067, 1093376176159, 1093376176159, 2623076354557, 2623076354557, 241599308325943, 241599308325943, 1604223576455477

Offset: 0

Author

Paul Curtz, Jan 23 2010

Keywords

• nonn
• frac

Comments

The generating function of the "original" Bernoulli numbers is

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(n) = 0, 1, 5/2, 31/6, 31/3, 619/30,... obeying c(n+1)-2*c(n) = A164555(n)/A027642(n).

a(n) is the numerator of c(n).

Crossrefs

Cf. A172031.

Programs

Mathematica

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 *)

Extensions

Edited and extended by R. J. Mathar, Mar 14 2010