cp's OEIS Frontend

A239315 Array read by antidiagonals: denominators of the core of the classical Bernoulli numbers.

%I A239315 #11 Apr 11 2014 06:44:08
%S A239315 15,15,15,105,105,105,21,105,105,21,105,105,105,105,105,15,105,105,
%T A239315 105,105,15,165,165,1155,231,1155,165,165,33,165,165,231,231,165,165,
%U A239315 33,15015,15015,15015,15015,15015,15015,15015,15015,15015
%N A239315 Array read by antidiagonals: denominators of the core of the classical Bernoulli numbers.
%C A239315 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:
%C A239315 2/15,     1/15,    -1/105,   -1/21,   -1/105,     1/15,   7/165,   -5/33,...
%C A239315 -1/15,  -8/105,    -4/105,   4/105,    8/105,   -4/165, -32/165,...
%C A239315 -1/105,  4/105,     8/105,   4/105, -116/1155, -28/165,...
%C A239315 1/21,    4/105,    -4/105, -32/231,   -16/231,...
%C A239315 -1/105, -8/105, -116/1155,  16/231,...
%C A239315 -1/15,  -4/165,    28/165,...
%C A239315 7/165,  32/165,...
%C A239315 5/33,... etc.
%C A239315 This is an autosequence of the second kind.
%C A239315 The antidiagonals are palindromes in absolute values.
%C A239315 a(n) are the denominators. Multiples of 3.
%C A239315 Sum of odd antidiagonals: 2/15, -2/21, 2/15, -10/33, 1382/1365,... = -2*A000367(n+2)/A001897(n+2).
%C A239315 The sum of the even antidiagonals is A000004.
%C A239315 2/15, 0, -2/21,... = -4*A027641(n+4)/A027642(n+4) = -4*A164555(n)/A027642(n+4) and others.
%e A239315 As a triangle:
%e A239315 15,
%e A239315 15,   15,
%e A239315 105, 105, 105,
%e A239315 21,  105, 105, 21,
%e A239315 105, 105, 105, 105, 105,
%e A239315 etc.
%t A239315 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-François Alcover_, Apr 11 2014 *)
%Y A239315 Cf. A085737/A085738, A168516/A168426 (autosequence), A027641, A176327/A176289, A235774, A165161/A051717(n+1).
%K A239315 nonn,tabl,frac
%O A239315 0,1
%A A239315 _Paul Curtz_, Mar 15 2014