A163259 Triangle T(n,k) read by rows: mod(A007318(n,k+1);A007318(n,k)).

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 4, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 5, 15, 6, 1, 0, 0, 0, 14, 0, 21, 7, 1, 0, 0, 4, 0, 14, 56, 28, 8, 1, 0, 0, 0, 12, 42, 0, 84, 36, 9, 1, 0, 0, 5, 30, 90, 42, 210, 120, 45, 10, 1, 0, 0, 0, 0, 0, 132, 0, 330, 165, 55, 11, 1, 0, 0, 6, 22, 55, 297, 132, 792, 495

Offset

1,12

Comments

The zeros in this table form the pattern of ones in A051731.

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows

Formula

T(n, k) = mod(binomial(n, k + 1), binomial(n, k)), for 0 <= k <= n, n>= 0. - G. C. Greubel, Dec 12 2016

Example

Table begins:
0
0...0
0...1...0
0...0...1...0
0...2...4...1...0
0...0...0...5...1...0
0...3...5..15...6...1...0
0...0..14...0..21...7...1...0
0...4...0..14..56..28...8...1...0
0...0..12..42...0..84..36...9...1...0
0...5..30..90..42.210.120..45..10...1...0

Mathematica

T[n_, k_] := Mod[Binomial[n, k + 1], Binomial[n, k]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]// Flatten (* G. C. Greubel, Dec 12 2016 *)

Crossrefs

Cf. A163260, A051731, A007318.

Sequence in context: A305570 A287651 A365951 * A309785 A188668 A366463

Adjacent sequences: A163256 A163257 A163258 * A163260 A163261 A163262

Keyword

nonn,tabl

Author

Mats Granvik, Jul 23 2009

Extensions

Corrected the formula in the title Mats Granvik, Jul 24 2009

Status

approved