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1, 4, 2, 6, 6, 3, 8, 12, 12, 4, 10, 20, 30, 20, 5, 12, 30, 60, 60, 30, 6, 14, 42, 105, 140, 105, 42, 7, 16, 56, 168, 280, 280, 168, 56, 8, 18, 72, 252, 504, 630, 504, 252, 72, 9, 20, 90, 360, 840, 1260, 1260, 840, 360, 90, 10
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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T(n, k) = (k+1)*binomial(n+1, k+1), with T(n, n) = n+1, T(n, 0) = 2*(n+1). - G. C. Greubel, Dec 07 2016
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EXAMPLE
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First few rows of the triangle are:
1;
4, 2;
6, 6, 3;
8, 12, 12, 4;
10, 20, 30, 20, 5;
12, 30, 60, 60, 30, 6;
14, 42, 105, 140, 105, 42, 7;
...
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MATHEMATICA
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T[n_, k_]:= If[k==n, n+1, If[k==0, 2*(n+1), (k+1)*Binomial[n+1, k+1]]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//flatten (* G. C. Greubel, Dec 07 2016 *)
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PROG
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(Sage)
if (n==0): return 1
elif (k==0): return 2*(n+1)
else: return (k+1)*binomial(n+1, k+1)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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