A174276 Denominator 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, 2, 6, 30, 70, 210, 2310, 10010, 6006, 510510, 461890, 9699690, 31870410, 74364290, 223092870, 6469693230, 6077590610, 200560490130, 200560490130, 494715875654, 674612557710, 60850052705442, 872184088778002, 13082761331670030

Offset: 0

Author

Paul Curtz, Mar 14 2010

Keywords

• nonn
• frac

Comments

The numerators are in A174289. 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(denom,%) ;

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, 23}] // Denominator (* Jean-François Alcover_, Aug 09 2012 *)