A129367 Triangle T(n, k) = A002415(n-k+3)*A002415(k+3), read by rows.

36, 120, 120, 300, 400, 300, 630, 1000, 1000, 630, 1176, 2100, 2500, 2100, 1176, 2016, 3920, 5250, 5250, 3920, 2016, 3240, 6720, 9800, 11025, 9800, 6720, 3240, 4950, 10800, 16800, 20580, 20580, 16800, 10800, 4950, 7260, 16500, 27000, 35280, 38416, 35280, 27000, 16500, 7260

Offset

0,1

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(n,k) = A002415(n-k+3)*A002415(k+3), where A002415(n) = n^2*(n^2-1)/12.

T(n, n-k) = T(n, k).

Example

Triangle begins as:
    36;
   120,   120;
   300,   400,   300;
   630,  1000,  1000,   630;
  1176,  2100,  2500,  2100,  1176;
  2016,  3920,  5250,  5250,  3920,  2016;
  3240,  6720,  9800, 11025,  9800,  6720,  3240;
  4950, 10800, 16800, 20580, 20580, 16800, 10800,  4950;
  7260, 16500, 27000, 35280, 38416, 35280, 27000, 16500, 7260;

Mathematica

A129367[n_, k_]:= Binomial[(n-k+3)^2, 2]*Binomial[(k+3)^2, 2]/36;
Table[A129367[n, k], {n, 0, 12}, {k, 0, n}]//Flatten

Prog

(Magma) [Binomial((n-k+3)^2, 2)*Binomial((k+3)^2, 2)/36: k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 31 2024
(SageMath)
def A129367(n, k): return binomial((n-k+3)^2, 2)*binomial((k+3)^2, 2)/36
flatten([[A129367(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Jan 31 2024

Crossrefs

Cf. A002415, A117662.

Sequence in context: A033575 A044287 A044668 * A350500 A287861 A242356

Adjacent sequences: A129364 A129365 A129366 * A129368 A129369 A129370

Keyword

nonn,tabl,easy,less

Author

Roger L. Bagula and Gary W. Adamson, Aug 25 2008

Extensions

Edited by G. C. Greubel, Jan 31 2024

Status

approved