A265603 Triangle read by rows, the denominators of the Bell transform of B(2n,1) where B(n,x) are the Bernoulli polynomials.

1, 1, 1, 1, 6, 1, 1, 30, 2, 1, 1, 42, 20, 1, 1, 1, 30, 63, 12, 3, 1, 1, 66, 1260, 504, 12, 2, 1, 1, 2730, 495, 360, 72, 4, 2, 1, 1, 6, 900900, 5940, 432, 2, 30, 3, 1, 1, 510, 15015, 1351350, 990, 80, 6, 10, 1, 1, 1, 798, 5105100, 360360, 154440, 1056, 80, 12, 2, 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..65.

Example

1,
1,    1,
1,    6,      1,
1,   30,      2,       1,
1,   42,     20,       1,   1,
1,   30,     63,      12,   3,  1,
1,   66,   1260,     504,  12,  2,  1,
1, 2730,    495,     360,  72,  4,  2,  1,
1,    6, 900900,    5940, 432,  2, 30,  3, 1,
1,  510,  15015, 1351350, 990, 80,  6, 10, 1, 1.

Maple

A265603_triangle := proc(n) local B, C, k;
B := BellMatrix(x -> bernoulli(2*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:
A265603_triangle(10);

Mathematica

BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
rows = 12;
B = BellMatrix[BernoulliB[2#, 1]&, rows];
Table[B[[n, k]] // Denominator, {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 27 2018, from Maple *)

Crossrefs

Cf. A265602 for the numerators, A265314 and A265315 for B(n,1).

Cf. A002445 (column 1).

Sequence in context: A201461 A340475 A368848 * A174186 A111578 A166349

Adjacent sequences: A265600 A265601 A265602 * A265604 A265605 A265606

Keyword

nonn,tabl,frac

Author

Peter Luschny, Jan 21 2016

Status

approved