A122496 T(n, m) = 2^m * binomial(-m, n), for 0 <= m <= n, n >= 0, triangle read by rows.

1, 0, -2, 0, 2, 12, 0, -2, -16, -80, 0, 2, 20, 120, 560, 0, -2, -24, -168, -896, -4032, 0, 2, 28, 224, 1344, 6720, 29568, 0, -2, -32, -288, -1920, -10560, -50688, -219648, 0, 2, 36, 360, 2640, 15840, 82368, 384384, 1647360, 0, -2, -40, -440, -3520, -22880, -128128, -640640, -2928640, -12446720

Offset

1,3

Links

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Formula

T(n, m) = 2^m * binomial(-m, n), for 0 <= m <= n, n >= 0. - G. C. Greubel, May 15 2019

Example

Triangle begins as:
  1;
  0, -2;
  0,  2,  12;
  0, -2, -16,  -80;
  0,  2,  20,  120,  560;
  0, -2, -24, -168, -896, -4032;

Mathematica

f[i_, k_, l_]:= Binomial[k-l, i-Min[k, l]]/2^(k-l);
Table[f[i, 0, l], {i, 0, 12}, {l, 0, i}] // Flatten (* modified by G. C. Greubel, May 15 2019 *)

Prog

(Magma) [[2^m*Binomial(-m, n): m in [0..n]]: n in [0..12]]; // G. C. Greubel, May 15 2019
(Sage) [[2^m*binomial(-m, n) for m in (0..n)] for n in (0..12)] # G. C. Greubel, May 15 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> 2^k*Binomial(-k, n) ))); # G. C. Greubel, May 15 2019

Crossrefs

Sequence in context: A211910 A250406 A107094 * A335756 A230813 A367074

Adjacent sequences: A122493 A122494 A122495 * A122497 A122498 A122499

Keyword

sign,easy,tabl

Author

Roger L. Bagula, Sep 14 2006

Extensions

Edited by N. J. A. Sloane, Oct 01 2006

Edited by G. C. Greubel, May 15 2019

Better name using formula given, Joerg Arndt, Jan 21 2024

Status

approved