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Search: id:A157011
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| A157011 |
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Riordan's general Eulerian recursion:m=0: ( A008292 is m=1); e(n,k,m)= (k + m)e(n - 1, k, m) + (n - k + 1 - m)e(n - 1, k - 1, m) |
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+0
1
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| 1, 1, 2, 1, 5, 4, 1, 9, 23, 8, 1, 14, 82, 93, 16, 1, 20, 234, 607, 343, 32, 1, 27, 588, 2991, 3800, 1189, 64, 1, 35, 1365, 12501, 30155, 21145, 3951, 128, 1, 44, 3010, 47058, 195626, 256500, 108286, 12749, 256, 1, 54, 6416, 165254, 1111910, 2456256
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums are:
{1, 3, 10, 41, 206, 1237, 8660, 69281, 623530, 6235301,...}.
This recursion set doesn't seem to produce the Eulerian 2nd A008517.
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, pp. 214-215
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FORMULA
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e(n,k,m)= (k + m)e(n - 1, k, m) + (n - k + 1 - m)e(n - 1, k - 1, m).
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EXAMPLE
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{1},
{1, 2},
{1, 5, 4},
{1, 9, 23, 8},
{1, 14, 82, 93, 16},
{1, 20, 234, 607, 343, 32},
{1, 27, 588, 2991, 3800, 1189, 64},
{1, 35, 1365, 12501, 30155, 21145, 3951, 128},
{1, 44, 3010, 47058, 195626, 256500, 108286, 12749, 256},
{1, 54, 6416, 165254, 1111910, 2456256, 1932216, 522387, 40295, 512}
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MATHEMATICA
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e[n_, 0, m_] := 1;
e[n_, k_, m_] := 0 /; k >= n;
e[n_, k_, m_] := (k + m)e[n - 1, k, m] + (n - k + 1 - m)e[n - 1, k - 1, m];
Table[Flatten[Table[Table[e[ n, k, m], {k, 0, n - 1}], {n, 1, 10}]], {m, 0, 10}]
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CROSSREFS
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A008517, A008292
Sequence in context: A128718 A112358 A126351 this_sequence A092821 A110552 A129161
Adjacent sequences: A157008 A157009 A157010 this_sequence A157012 A157013 A157014
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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 21 2009
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