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

0,1

Comments

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

Links

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

Formula

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

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 *)

Crossrefs

Cf. A085737, A085738, A162298, A162299.

Sequence in context: A343390 A105437 A323952 * A333699 A088100 A097359

Adjacent sequences: A168137 A168138 A168139 * A168141 A168142 A168143

Keyword

sign,tabl

Author

Juri-Stepan Gerasimov, Nov 19 2009

Extensions

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

Status

approved