A172032 Numerator of the rational sequence c(n) defined by c(n+1) - 2*c(n) = Bernoulli number B_n (A027641/A027642).

0, 1, 3, 19, 19, 379, 379, 3539, 3539, 42461, 42461, 1868459, 1868459, 32384089, 32384089, 388644103, 388644103, 26424178387, 26424178387, 669590253599, 669590253599, 1605990140413, 1605990140413, 148027376624695, 148027376624695, 980410698447157

Offset: 0

Author

Paul Curtz, Jan 23 2010

Keywords

• nonn
• frac

Comments

c(n) starts with: 0, 1, 3/2, 19/6, 19/3,3 79/30, 379/15, 3539/70, 3539/35, 42461/210, 42461/105, ...

The corresponding denominator is A172031 (also denominator of rational sequence defined in A172030).

It appears that A172030/A172031 - A172032/A172031 = 0, 0, 1, 2, 4, 8, 16, ... that is A131577 prepended with 0.

Programs

PARI

aseq(m) = {cvec = vector(m); cvec[1] = 0; for (i=2, m, cvec[i] = bernfrac(i-2) + 2*cvec[i-1];);} \\Michel Marcus, Feb 03 2013

Extensions

Edited by Michel Marcus, Feb 03 2013