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A256675 Denominators of the inverse binomial transform of Bernoulli(n+2).

%I A256675 #22 Apr 19 2015 22:34:32
%S A256675 6,6,15,15,105,21,105,15,165,33,15015,1365,1365,3,255,255,33915,399,
%T A256675 21945,165,3795,69,31395,1365,1365,3,435,435,1038345,7161,608685,255,
%U A256675 255,3,959595,959595,959595,3,6765,6765,2036265,903,103845,345,16215,141,1090635
%N A256675 Denominators of the inverse binomial transform of Bernoulli(n+2).
%C A256675 Difference table of B(n+2):
%C A256675 1/6,        0,  -1/30,     0,   1/42,     0, -1/30, ...
%C A256675 -1/6,   -1/30,   1/30,  1/42,  -1/42, -1/30,   ...
%C A256675 2/15,    1/15, -1/105, -1/21, -1/105,   ...
%C A256675 -1/15, -8/105, -4/105, 4/105,    ...
%C A256675 -1/105, 4/105,  8/105,   ...
%C A256675 1/21,   4/105,    ...
%C A256675 -1/105,   ...
%C A256675 ...
%C A256675 a(n) is the denominator of the n-th term of the first column.
%C A256675 a(n+2) is the denominator of the n-th term of the third row.
%C A256675 See A239315(n), which is the table without the first two rows.
%C A256675 Inverse binomial transform: 1/6, -1/6, 2/15, -1/15, -1/105, 1/21, -1/105, -1/15, 7/165, 5/33, -2663/15015, ... .
%F A256675 a(2n) = A029765(n).
%F A256675 a(2n+3) = A001897(n+2).
%F A256675 a(2n)/a(2n+1) = A177735(n).
%F A256675 a(2n+4)/a(2n+3) = A177735(n+3).
%t A256675 max = 42; bb = Table[BernoulliB[n+2], {n, 0, max}]; dd = Table[Differences[bb, n], {n, 0, max}]; dd[[All, 1]] // Denominator (* _Jean-François Alcover_, Apr 09 2015 *)
%o A256675 (PARI) lista(nn) = {A = vector(nn, n, bernfrac(n+1)); for (i=1, #A-1, for(j=0,i-1,A[i+1]-=binomial(i,j)*A[j+1])); for (i=1, #A, print1(denominator(A[i]), ", "));} \\ _Michel Marcus_, Apr 08 2015
%Y A256675 Cf. A190339, A239315, A029765, A001897, A141459, A172087, A168516, A177735, A256595.
%K A256675 nonn
%O A256675 0,1
%A A256675 _Paul Curtz_, Apr 07 2015