A256675 - OEIS

%I #22 Apr 19 2015 22:34:32

%S 6,6,15,15,105,21,105,15,165,33,15015,1365,1365,3,255,255,33915,399,

%T 21945,165,3795,69,31395,1365,1365,3,435,435,1038345,7161,608685,255,

%U 255,3,959595,959595,959595,3,6765,6765,2036265,903,103845,345,16215,141,1090635

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

%C Difference table of B(n+2):

%C 1/6,        0,  -1/30,     0,   1/42,     0, -1/30, ...

%C -1/6,   -1/30,   1/30,  1/42,  -1/42, -1/30,   ...

%C 2/15,    1/15, -1/105, -1/21, -1/105,   ...

%C -1/15, -8/105, -4/105, 4/105,    ...

%C -1/105, 4/105,  8/105,   ...

%C 1/21,   4/105,    ...

%C -1/105,   ...

%C ...

%C a(n) is the denominator of the n-th term of the first column.

%C a(n+2) is the denominator of the n-th term of the third row.

%C See A239315(n), which is the table without the first two rows.

%C 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 a(2n) = A029765(n).

%F a(2n+3) = A001897(n+2).

%F a(2n)/a(2n+1) = A177735(n).

%F a(2n+4)/a(2n+3) = A177735(n+3).

%t 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 (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 Cf. A190339, A239315, A029765, A001897, A141459, A172087, A168516, A177735, A256595.

%K nonn

%O 0,1

%A _Paul Curtz_, Apr 07 2015