A174289 Numerator of the n-th term of the inverse binomial transform of 1, 1/2, B_4, B_6, B_8,..., a modified Bernoulli sequence.

1, -1, 1, -1, 11, -137, 4157, -44879, 74351, -23262859, 113428851, -18122193779, 593728889477, -17199344405209, 773610521462677, -398027397442098469, 7730820046943979149, -6072430937404995879629, 164713122370768078443379

Offset: 0

Author

Paul Curtz, Mar 15 2010

Keywords

• frac
• sign

Comments

The denominators are in A174276. The input sequence starts 1, 1/2, 1/6, -1/30, 1/42....

The inverse binomial transform generates 1, -1/2, 1/6, -1/30, 11/70, -137/210, 4157/2310,...

Crossrefs

Cf. A000367, A164555, A006954.

Programs

Maple

read("transforms") ;
L := [1,1/2,seq(bernoulli(2*i),i=1..30)] ;BINOMIALi(L) ; apply(numer,%) ; # R. J. Mathar, Dec 02 2010

Mathematica

b[0]=1; b[1]=1/2; b[n_] := BernoulliB[2n-2]; a[n_] := Sum[(-1)^(n-k)*Binomial[n, k]*b[k], {k, 0, n}]; Table[a[n], {n, 0, 18}] // Numerator (* Jean-François Alcover_, Aug 09 2012 *)