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Search: id:A156139
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| A156139 |
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A triangular recursion: A(n,k)=(2*n - k - 1)*A(n - 1, k - 1) + (k + 1)*A(n - 1, k) |
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+0
3
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| 1, 1, 1, 1, 6, 1, 1, 23, 28, 1, 1, 76, 250, 145, 1, 1, 237, 1608, 2475, 876, 1, 1, 722, 8802, 26847, 25056, 6139, 1, 1, 2179, 43872, 231057, 418806, 268477, 49120, 1, 1, 6552, 205994, 1725621, 5285520, 6486205, 3077730, 442089, 1, 1, 19673, 928808
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 2, 8, 53, 473, 5198, 67568, 1013513, 17229713, 327364538,...}.
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REFERENCES
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Leonard M. Smiley,"Completion of a Rational Function Sequence of Carlitz,http://www.math.uaa.alaska.edu/~smiley/BSfront.html,page 2.
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FORMULA
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A(n,k)=(2*n - k - 1)*A(n - 1, k - 1) + (k + 1)*A(n - 1, k)
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EXAMPLE
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{1},
{1, 1},
{1, 6, 1},
{1, 23, 28, 1},
{1, 76, 250, 145, 1},
{1, 237, 1608, 2475, 876, 1},
{1, 722, 8802, 26847, 25056, 6139, 1},
{1, 2179, 43872, 231057, 418806, 268477, 49120, 1},
{1, 6552, 205994, 1725621, 5285520, 6486205, 3077730, 442089, 1},
{1, 19673, 928808, 11718015, 55871814, 114115195, 102456300, 37833831, 4420900, 1}
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MATHEMATICA
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A[n_, 1] := 1; A[n_, n_] := 1;
A[n_, k_] := (2*n - k - 1)*A[n - 1, k - 1] + (k + 1)*A[n - 1, k];
TableForm[Table[A[n, k], {n, 10}, {k, n}], TableAlignments -> Right];
Table[Table[A[n, k], {k, n}], {n, 10}];
Flatten[%]
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CROSSREFS
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Adjacent sequences: A156136 A156137 A156138 this_sequence A156140 A156141 A156142
Sequence in context: A152936 A152969 A060187 this_sequence A155863 A035348 A140945
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 04 2009
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