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A172030 Numerators of the sequence with g.f. x*B(x)/(1-2*x), where B(x) denotes the "original" Bernoulli numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Apr 15 2013 *)

CROSSREFS

Cf. A172031.

Sequence in context: A255677 A256153 A238196 * A042837 A162173 A027761

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

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)