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1, 3, 2, 8, 4, 3, 20, 6, 9, 4, 48, 8, 18, 16, 5, 112, 10, 30, 40, 25, 6, 256, 12, 45, 80, 75, 36, 7, 576, 14, 63, 140, 175, 126, 49, 8, 1280, 16, 84, 224, 350, 336, 196, 64, 9, 2816, 18, 108, 336, 630, 756, 588, 288, 81, 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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COMMENTS
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Binomial transform of triangle A103516.
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LINKS
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FORMULA
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Sum_{k=0..n} T(n, k) = A099035(n+1).
T(n, k) = (k+1)*binomial(n, k), with T(n, 0) = (n+2)*2^(n-1), T(n, n) = 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;
3, 2;
8, 4, 3;
20, 6, 9, 4;
48, 8, 18, 16, 5;
112, 10, 30, 40, 25, 6;
256, 12, 45, 80, 75, 36, 7;
...
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MATHEMATICA
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T[n_, k_]:= If[n==0, 1, If[k==0, (n+2)*2^(n-1), (k+1)*Binomial[n, k]]];
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 (n+2)*2^(n-1)
else: return (k+1)*binomial(n, k)
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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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