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A168140 Sum of n-th numerator and n-th denominator in triangle formed from Bernoulli numbers.

%I A168140 #18 May 21 2020 10:58:14
%S A168140 2,3,3,7,4,7,1,7,7,1,29,31,17,31,29,1,29,16,16,29,1,43,41,104,113,104,
%T A168140 41,43,1,43,20,109,109,20,43,1,29,31,104,101,113,101,104,31,29,1,29,
%U A168140 16,97,109,109,97,16,29,1,71,61,172,169,1039,263,1039,169,172,61,71,1,71,28,197,137,247,247,137,197,28,71,1
%N A168140 Sum of n-th numerator and n-th denominator in triangle formed from Bernoulli numbers.
%C A168140 Terms become negative later in the sequence. - _R. J. Mathar_, Apr 14 2010
%H A168140 Alois P. Heinz, <a href="/A168140/b168140.txt">Rows n = 0..140, flattened</a>
%F A168140 a(n) = A085737(n) + A085738(n).
%p A168140 b := proc(n, k) option remember; if k = 0 then (-1)^n*bernoulli(n) ; elif k > n/2 then procname(n, n-k) ; else procname(n-1, k-1)-procname(n, k-1) ; end if; end proc: T := proc(n, k) numer(b(n, k))+denom(b(n, k)) ; end proc: seq(seq(T(n,k), k=0..n), n=0..10); # _R. J. Mathar_, Apr 14 2010
%t A168140 b[n_, 0] := (-1)^n BernoulliB[n];
%t A168140 b[n_, k_] := b[n, k] = b[n - 1, k - 1] - b[n, k - 1];
%t A168140 T[n_, k_] := Numerator[b[n, k]] + Denominator[b[n, k]];
%t A168140 Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, May 21 2020 *)
%Y A168140 Cf. A085737, A085738, A162298, A162299.
%K A168140 sign,tabl
%O A168140 0,1
%A A168140 _Juri-Stepan Gerasimov_, Nov 19 2009
%E A168140 A 109 duplicated, 1049 replaced with 1039 by _R. J. Mathar_, Apr 14 2010