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

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

Offset: 0

Author

Juri-Stepan Gerasimov, Nov 19 2009

Keywords

• sign
• tabl

Comments

Terms become negative later in the sequence. - R. J. Mathar, Apr 14 2010

Links

• Alois P. Heinz, Rows n = 0..140, flattened

Crossrefs

Cf. A085737, A085738, A162298, A162299.

Programs

Maple

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

Mathematica

b[n_, 0] := (-1)^n BernoulliB[n];
b[n_, k_] := b[n, k] = b[n - 1, k - 1] - b[n, k - 1];
T[n_, k_] := Numerator[b[n, k]] + Denominator[b[n, k]];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 21 2020 *)

Formula

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

Extensions

A 109 duplicated, 1049 replaced with 1039 by R. J. Mathar, Apr 14 2010