A176250 Numerators of the fractions defined by 2 minus partial sums of the "original" Bernoulli numbers.

2, 1, 1, 1, 1, 11, 11, 12, 12, 79, 79, 347, 347, 5541, 5541, -9206, -9206, 3307613, 3307613, -78393123, -78393123, 932396477, 932396477, -127419293864, -127419293864, 6013748071263, 6013748071263

Offset: 0

Author

Paul Curtz, Apr 13 2010

Keywords

• sign
• frac

Comments

We define the sequence f(n) = 2, 1, 1/2, 1/3, 1/3, 11/30, 11/30, ... for n >= 0 as 2-Sum_{i=0..n-1} A164555(i)/A027642(i). The current sequence shows the numerators of f.

Comparison with a similar sequence of fractions g(n) = A100649(n)/A100650(n): f(n) = g(n-1) - 1 for n > 1.

Crossrefs

Cf. A100650 (denominators), A164555, A027642.

Programs

Maple

B := proc(n) if n = 1 then -bernoulli(n); else bernoulli(n); end if; end proc:
A176250 := proc(n) 2-add(B(i),i=0..n-1) ; numer(%) ;end proc:
seq(A176250(n),n=0..40) ; # R. J. Mathar, Jun 01 2011