A265315 Triangle read by rows, the denominators of the Bell transform of B(n,1) where B(n,x) are the Bernoulli polynomials.

1, 1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 1, 12, 1, 1, 1, 30, 6, 12, 1, 1, 1, 1, 90, 8, 12, 2, 1, 1, 42, 20, 360, 8, 12, 2, 1, 1, 1, 315, 45, 720, 6, 6, 1, 1, 1, 30, 7, 3780, 20, 240, 2, 2, 1, 1, 1, 1, 350, 7, 756, 32, 240, 4, 2, 2, 1, 1, 66, 12, 6300, 1512, 6048, 96, 240, 4, 1, 2, 1

Offset

0,5

Comments

For the definition of the Bell transform see A264428 and the link given there.

Links

Table of n, a(n) for n=0..77.

Example

1,
1,  1,
1,  2,   1,
1,  6,   2,    1,
1,  1,  12,    1,   1,
1, 30,   6,   12,   1,   1,
1,  1,  90,    8,  12,   2,   1,
1, 42,  20,  360,   8,  12,   2, 1,
1,  1, 315,   45, 720,   6,   6, 1, 1,
1, 30,   7, 3780,  20, 240,   2, 2, 1, 1,
1,  1, 350,    7, 756,  32, 240, 4, 2, 2, 1.

Maple

A265315_triangle := proc(n) local B, C, k;
B := BellMatrix(x -> bernoulli(x, 1), n);  # see A264428
for k from 1 to n do
   C := LinearAlgebra:-Row(B, k):
   print(seq(denom(C[j]), j=1..k))
od end:
A265315_triangle(12);

Mathematica

BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
rows = 12;
B = BellMatrix[Function[x, BernoulliB[x, 1]], rows];
Table[B[[n, k]] // Denominator, {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 26 2018, from Maple *)

Crossrefs

Cf. A265314 for the numerators, A265602 and A265603 for B(2n,1).

Cf. A027642 (column 1).

Sequence in context: A322128 A125731 A123361 * A179380 A107106 A178249

Adjacent sequences: A265312 A265313 A265314 * A265316 A265317 A265318

Keyword

nonn,tabl,frac

Author

Peter Luschny, Jan 22 2016

Status

approved