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A214810
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Triangle read by rows: T(n,k) (n>=1, 0 <= k <= p where p = n-th prime) = Bell(k) mod p (cf. A000110).
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4
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1, 1, 0, 1, 1, 2, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 5, 1, 3, 0, 2, 1, 1, 2, 5, 4, 8, 5, 8, 4, 5, 2, 2, 1, 1, 2, 5, 2, 0, 8, 6, 6, 9, 2, 9, 11, 2, 1, 1, 2, 5, 15, 1, 16, 10, 9, 16, 1, 15, 11, 6, 15, 11, 14, 2, 1, 1, 2, 5, 15, 14, 13, 3, 17, 0, 18, 4, 5, 7, 14, 16, 15, 1, 10, 2, 1, 1, 2, 5, 15, 6, 19, 3, 0, 10, 9, 1, 20, 1, 12, 9, 5, 6, 6, 9, 4, 16, 22, 2, 1, 1, 2, 5, 15, 23, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,6
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COMMENTS
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The n-th row gives Bell numbers mod prime(n) and has length prime(n)+1.
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LINKS
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EXAMPLE
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Triangle begins:
[1, 1, 0],
[1, 1, 2, 2],
[1, 1, 2, 0, 0, 2],
[1, 1, 2, 5, 1, 3, 0, 2],
[1, 1, 2, 5, 4, 8, 5, 8, 4, 5, 2, 2],
[1, 1, 2, 5, 2, 0, 8, 6, 6, 9, 2, 9, 11, 2],
[1, 1, 2, 5, 15, 1, 16, 10, 9, 16, 1, 15, 11, 6, 15, 11, 14, 2],
[1, 1, 2, 5, 15, 14, 13, 3, 17, 0, 18, 4, 5, 7, 14, 16, 15, 1, 10, 2],
...
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MAPLE
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T:= n-> (p-> seq(combinat[bell](k) mod p, k=0..p))(ithprime(n)):
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MATHEMATICA
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A214810row[n_]:=Mod[BellB[Range[0, Prime[n]]], Prime[n]]; Array[A214810row, 50] (* Paolo Xausa, Aug 07 2023 *)
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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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