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A159623
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Triangle read by rows: T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 1.
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4
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 12, 4, 1, 1, 5, 20, 20, 5, 1, 1, 6, 30, 120, 30, 6, 1, 1, 7, 42, 210, 210, 42, 7, 1, 1, 8, 56, 336, 1680, 336, 56, 8, 1, 1, 9, 72, 504, 3024, 3024, 504, 72, 9, 1, 1, 10, 90, 720, 5040, 30240, 5040, 720, 90, 10, 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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The row sums are: {1, 2, 4, 8, 22, 52, 194, 520, 2482, 7220, 41962,...}.
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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 = 1.
T(n, n-k) = T(n, k).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 12, 4, 1;
1, 5, 20, 20, 5, 1;
1, 6, 30, 120, 30, 6, 1;
1, 7, 42, 210, 210, 42, 7, 1;
1, 8, 56, 336, 1680, 336, 56, 8, 1;
1, 9, 72, 504, 3024, 3024, 504, 72, 9, 1;
1, 10, 90, 720, 5040, 30240, 5040, 720, 90, 10, 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, 1], {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, 1) 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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