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A265603 Triangle read by rows, the denominators of the Bell transform of B(2n,1) where B(n,x) are the Bernoulli polynomials. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
For the definition of the Bell transform see A264428 and the link given there.
LINKS
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
KEYWORD
nonn,tabl,frac
AUTHOR
Peter Luschny, Jan 21 2016
STATUS
approved

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Last modified June 14 12:19 EDT 2024. Contains 373400 sequences. (Running on oeis4.)