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A129367
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Triangle T(n, k) = A002415(n-k+3)*A002415(k+3), read by rows.
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2
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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
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listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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T(n, n-k) = T(n, k).
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EXAMPLE
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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;
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MATHEMATICA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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