A175779 Triangle T(n,m) read by rows: numerator of 1/(n-m)^2 - 1/n^2.

1, 0, 1, 0, 3, 1, 0, 5, 8, 1, 0, 7, 3, 15, 1, 0, 9, 16, 21, 24, 1, 0, 11, 5, 1, 2, 35, 1, 0, 13, 24, 33, 40, 45, 48, 1, 0, 15, 7, 39, 3, 55, 15, 63, 1, 0, 17, 32, 5, 56, 65, 8, 77, 80

Offset

0,5

Comments

T(n,0) is set to zero at the pole m=0. T(n,n) is otherwise set to 1 at the pole n=m.

This is the triangle A061035 augmented by a diagonal of 1's.

Essentially the same information is in A120072, A166492, A172157 and A174233.

Links

G. C. Greubel, Rows n=0..100 of triangle, flattened

Example

The triangle starts in row n=0 with columns 0<=m<=n as:
.1.
.0..1.
.0..3..1.
.0..5..8..1.
.0..7..3.15..1.
.0..9.16.21.24..1.
.0.11..5..1..2.35..1.
.0.13.24.33.40.45.48..1.
.0.15..7.39..3.55.15.63..1.
.0.17.32..5.56.65..8.77.80..1.
.0.19..9.51..4..3.21.91..6.99..1.

Mathematica

T[n_, n_] := 1; T[n_, k_] := 1/(n - k)^2 - 1/n^2; Table[Numerator[T[n, k]], {n, 0, 20}, {k, 0, n}] // Flatten  (* G. C. Greubel, Sep 19 2018 *)

Crossrefs

Cf. A172157, A166925, A171522 (denominators)

Sequence in context: A329989 A110032 A201667 * A280819 A300280 A135670

Adjacent sequences: A175776 A175777 A175778 * A175780 A175781 A175782

Keyword

nonn,frac,tabl

Author

Paul Curtz, Dec 04 2010

Status

approved