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

0,3

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).

Links

Table of n, a(n) for n=0..25.

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 *)

Crossrefs

Cf. A172031.

Sequence in context: A256153 A238196 A352347 * A042837 A354881 A162173

Adjacent sequences: A172027 A172028 A172029 * A172031 A172032 A172033

Keyword

nonn,frac

Author

Paul Curtz, Jan 23 2010

Extensions

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

Status

approved