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1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 6, 10, 6, 1, 1, 24, 49, 49, 24, 1, 1, 110, 248, 298, 248, 110, 1, 1, 545, 1308, 1749, 1749, 1308, 545, 1, 1, 2877, 7229, 10421, 11611, 10421, 7229, 2877, 1, 1, 16114, 41998, 64114, 77134, 77134, 64114, 41998, 16114, 1, 1, 95496
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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COMMENTS
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Row sums are:
1, 2, 3, 6, 24, 148, 1016, 7206, 52667, 398722, 3137084,...
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REFERENCES
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This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/BellNumber.nb.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 80.
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LINKS
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Table of n, a(n) for n=0..56.
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FORMULA
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t(n,m)=A033306(n,m)-A033306(n,0)+1
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EXAMPLE
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{1},
{1, 1},
{1, 1, 1},
{1, 2, 2, 1},
{1, 6, 10, 6, 1},
{1, 24, 49, 49, 24, 1},
{1, 110, 248, 298, 248, 110, 1},
{1, 545, 1308, 1749, 1749, 1308, 545, 1},
{1, 2877, 7229, 10421, 11611, 10421, 7229, 2877, 1},
{1, 16114, 41998, 64114, 77134, 77134, 64114, 41998, 16114, 1},
{1, 95496, 256626, 410226, 523476, 565434, 523476, 410226, 256626, 95496, 1}
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MATHEMATICA
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b[0] := 1;
b[n_] := b[n] = Total[Table[b[k]Binomial[n - 1, k], {k, 0, n - 1}]];
a = b /@ Range[0, 70];
t[n_, m_] := Binomial[n, m]*a[[m + 1]]*a[[n - m + 1]];
Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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A033306
Sequence in context: A127452 A135879 A176224 * A138169 A139331 A173886
Adjacent sequences: A174637 A174638 A174639 * A174641 A174642 A174643
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Mar 25 2010
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STATUS
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approved
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