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A129367 Triangle T(n, k) = A002415(n-k+3)*A002415(k+3), read by rows. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
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
Sequence in context: A033575 A044287 A044668 * A350500 A287861 A242356
KEYWORD
nonn,tabl,easy,less
AUTHOR
EXTENSIONS
Edited by G. C. Greubel, Jan 31 2024
STATUS
approved

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)