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A239315 Array read by antidiagonals: denominators of the core of the classical Bernoulli numbers. 5
15, 15, 15, 105, 105, 105, 21, 105, 105, 21, 105, 105, 105, 105, 105, 15, 105, 105, 105, 105, 15, 165, 165, 1155, 231, 1155, 165, 165, 33, 165, 165, 231, 231, 165, 165, 33, 15015, 15015, 15015, 15015, 15015, 15015, 15015, 15015, 15015 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

We consider the autosequence A164555(n)/A027642(n) (see A190339(n)) and its difference table without the first two rows and the first two columns:

2/15,     1/15,    -1/105,   -1/21,   -1/105,     1/15,   7/165,   -5/33,...

-1/15,  -8/105,    -4/105,   4/105,    8/105,   -4/165, -32/165,...

-1/105,  4/105,     8/105,   4/105, -116/1155, -28/165,...

1/21,    4/105,    -4/105, -32/231,   -16/231,...

-1/105, -8/105, -116/1155,  16/231,...

-1/15,  -4/165,    28/165,...

7/165,  32/165,...

5/33,... etc.

This is an autosequence of the second kind.

The antidiagonals are palindromes in absolute values.

a(n) are the denominators. Multiples of 3.

Sum of odd antidiagonals: 2/15, -2/21, 2/15, -10/33, 1382/1365,... = -2*A000367(n+2)/A001897(n+2).

The sum of the even antidiagonals is A000004.

2/15, 0, -2/21,... = -4*A027641(n+4)/A027642(n+4) = -4*A164555(n)/A027642(n+4) and others.

LINKS

Table of n, a(n) for n=0..44.

EXAMPLE

As a triangle:

15,

15,   15,

105, 105, 105,

21,  105, 105, 21,

105, 105, 105, 105, 105,

etc.

MATHEMATICA

max = 12; tb = Table[BernoulliB[n], {n, 0, max}]; td = Table[Differences[tb, n][[3 ;; -1]], {n, 2, max - 1}]; Table[td[[n - k + 1, k]] // Denominator, {n, 1, max - 3}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Apr 11 2014 *)

CROSSREFS

Cf. A085737/A085738, A168516/A168426 (autosequence), A027641, A176327/A176289, A235774, A165161/A051717(n+1).

Sequence in context: A225917 A140806 A085321 * A003890 A040211 A003891

Adjacent sequences:  A239312 A239313 A239314 * A239316 A239317 A239318

KEYWORD

nonn,tabl,frac

AUTHOR

Paul Curtz, Mar 15 2014

STATUS

approved

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Last modified April 20 03:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)