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A174378
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Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 4, read by rows.
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4
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1, 1, 1, 1, 8, 1, 1, 12, 12, 1, 1, 16, 192, 16, 1, 1, 20, 320, 320, 20, 1, 1, 24, 480, 7680, 480, 24, 1, 1, 28, 672, 13440, 13440, 672, 28, 1, 1, 32, 896, 21504, 430080, 21504, 896, 32, 1, 1, 36, 1152, 32256, 774144, 774144, 32256, 1152, 36, 1, 1, 40, 1440, 46080, 1290240, 30965760, 1290240, 46080, 1440, 40, 1
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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Row sums are: {1, 2, 10, 26, 226, 682, 8690, 28282, 474946, 1615178, ...}.
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LINKS
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FORMULA
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T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 2.
T(n, n-k) = T(n, k).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 8, 1;
1, 12, 12, 1;
1, 16, 192, 16, 1;
1, 20, 320, 320, 20, 1;
1, 24, 480, 7680, 480, 24, 1;
1, 28, 672, 13440, 13440, 672, 28, 1;
1, 32, 896, 21504, 430080, 21504, 896, 32, 1;
1, 36, 1152, 32256, 774144, 774144, 32256, 1152, 36, 1;
1, 40, 1440, 46080, 1290240, 30965760, 1290240, 46080, 1440, 40, 1;
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MATHEMATICA
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T[n_, k_, q_]:= If[Floor[n/2]>=k, n!*q^k/(n-k)!, n!*q^(n-k)/k!];
Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten
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PROG
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(Sage)
f=factorial
def T(n, k, q): return f(n)*q^k/f(n-k) if ((n//2)>k-1) else f(n)*q^(n-k)/f(k)
flatten([[T(n, k, 4) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Nov 28 2021
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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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