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A317644
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Triangle read by rows: multiplicative version of Pascal's triangle except n-th row begins and ends with (n+1)-st prime.
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0
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2, 3, 3, 5, 9, 5, 7, 45, 45, 7, 11, 315, 2025, 315, 11, 13, 3465, 637875, 637875, 3465, 13, 17, 45045, 2210236875, 406884515625, 2210236875, 45045, 17, 19, 765765, 99560120034375, 899311160300888671875, 899311160300888671875, 99560120034375, 765765, 19, 23, 14549535, 76239655318123171875, 89535527067809533413858673095703125, 808760563041730681160065242862701416015625, 89535527067809533413858673095703125, 76239655318123171875, 14549535, 23
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graph;
refs;
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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(End)
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EXAMPLE
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Triangle begins:
2;
3, 3;
5, 9, 5;
7, 45, 45, 7;
11, 315, 2025, 315, 11;
13, 3465, 637875, 637875, 3465, 13;
...
Formatted as a symmetric triangle:
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2
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3 3
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5 9 5
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7 45 45 7
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11 315 2025 315 11
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13 3465 637875 637875 3465 13
...
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MATHEMATICA
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t = {{2}};
Table[AppendTo[
t, {Prime[i],
Table[
t[[i - 1]][[j]]*t[[i - 1]][[j + 1]], {j,
1, (t[[i - 1]] // Length) - 1}], Prime[i]} // Flatten], {i, 2, 10}] //
Last // Flatten
t={}; Do[r={}; Do[If[k==0||k==n, m=Prime[n + 1], m=t[[n, k]]t[[n, k + 1]]]; r=AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t (* Vincenzo Librandi, Sep 03 2018 *)
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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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