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

6, 6, 15, 15, 105, 21, 105, 15, 165, 33, 15015, 1365, 1365, 3, 255, 255, 33915, 399, 21945, 165, 3795, 69, 31395, 1365, 1365, 3, 435, 435, 1038345, 7161, 608685, 255, 255, 3, 959595, 959595, 959595, 3, 6765, 6765, 2036265, 903, 103845, 345, 16215, 141, 1090635

Offset: 0

Author

Paul Curtz, Apr 07 2015

Keywords

• nonn

Comments

Difference table of B(n+2):

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

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

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

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

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

1/21, 4/105, ...

-1/105, ...

...

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

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

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

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, ... .

Crossrefs

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

Programs

Mathematica

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 *)

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

Formula

a(2n) = A029765(n).

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

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

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