A174263 Numerator of the n-th term of the inverse Binomial Transform of the Bernoulli sequence prefixed with 0.

0, 1, -5, 14, -23, 349, -499, 793, -1038, 7901, -9791, 65488, -78193, 795259, -925389, 1615811, -1841036, 67142767, -75821437, 358067518, -388783203, -521129621, 480390923, 133108162049

Offset: 0

Author

Paul Curtz, Mar 14 2010

Keywords

• sign
• frac

Comments

The inverse binomial transform of 0, 1, -1/2, 1/6, 0, ... is A(n) = 0, 1, -5/2, 14/3, -23/3, ... The current sequence is defined by the numerators; the denominators are A100650(n).

There is a connection to the sequence b(n) = 0, 1, 1/2, 1/6, 0, -1/30, ... of modified Bernoulli numbers [b(0)=0, b(2) = -Bernoulli(1), b(n) = Bernoulli(n-1) if n <> 2] discussed in A165142: The inverse binomial transform of b(n) is c(n) = 0, 1, -3/2, 5/3, -5/3, 49/30, -49/30, ..., and c(n) - A(n) = (-1)^n*A000217(n-1).

Crossrefs

Cf. A164558.

Programs

Maple

read("transforms") ;
A174264 := proc(n) local b; b := [0,seq(bernoulli(i),i=0..n+1)] ; BINOMIALi(b) ; numer(op(n+1,%)) ; end proc:
seq(A174264(n),n=0..30) ; # R. J. Mathar, Jan 21 2011