A168140 - OEIS

%I #18 May 21 2020 10:58:14

%S 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 41,43,1,43,20,109,109,20,43,1,29,31,104,101,113,101,104,31,29,1,29,

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

%C Terms become negative later in the sequence. - _R. J. Mathar_, Apr 14 2010

%H Alois P. Heinz, <a href="/A168140/b168140.txt">Rows n = 0..140, flattened</a>

%F a(n) = A085737(n) + A085738(n).

%p 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 b[n_, 0] := (-1)^n BernoulliB[n];

%t b[n_, k_] := b[n, k] = b[n - 1, k - 1] - b[n, k - 1];

%t T[n_, k_] := Numerator[b[n, k]] + Denominator[b[n, k]];

%t Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, May 21 2020 *)

%Y Cf. A085737, A085738, A162298, A162299.

%K sign,tabl

%O 0,1

%A _Juri-Stepan Gerasimov_, Nov 19 2009

%E A 109 duplicated, 1049 replaced with 1039 by _R. J. Mathar_, Apr 14 2010