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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.
4

%I #7 Aug 09 2012 06:24:25

%S 1,2,6,30,70,210,2310,10010,6006,510510,461890,9699690,31870410,

%T 74364290,223092870,6469693230,6077590610,200560490130,200560490130,

%U 494715875654,674612557710,60850052705442,872184088778002,13082761331670030

%N 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.

%C The numerators are in A174289. The input sequence starts 1, 1/2, 1/6, -1/30, 1/42....

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

%p read("transforms") ; L := [1,1/2,seq(bernoulli(2*i),i=1..30)] ; BINOMIALi(L) ; apply(denom,%) ;

%t 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 *)

%Y Cf. A000367, A164555, A006954.

%K nonn,frac

%O 0,2

%A _Paul Curtz_, Mar 14 2010