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Search: id:A156184
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| A156184 |
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A generalized recursion triangle sequence : m=1; t(n,k)=(k + m - 1)*t(n - 1, k, m) + (m*n - k + 1 - m)*t(n - 1, k - 1, m). |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 16, 7, 1, 1, 11, 53, 53, 11, 1, 1, 16, 150, 318, 150, 16, 1, 1, 22, 380, 1554, 1554, 380, 22, 1, 1, 29, 892, 6562, 12432, 6562, 892, 29, 1, 1, 37, 1987, 25038, 82538, 82538, 25038, 1987, 37, 1, 1, 46, 4270, 89023, 480380, 825380, 480380
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:A054091;
{1, 2, 4, 10, 32, 130, 652, 3914, 27400, 219202, 1972820,...}.
The sequence comes from a generalization of the recurrence for A008517.
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REFERENCES
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Weisstein, Eric W. "Second-Order Eulerian Triangle." http://mathworld.wolfram.com/Second-OrderEulerianTriangle.html
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FORMULA
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t(n,k)=(k + m - 1)*t(n - 1, k, m) + (m*n - k + 1 - m)*t(n - 1, k - 1, m).
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 4, 4, 1},
{1, 7, 16, 7, 1},
{1, 11, 53, 53, 11, 1},
{1, 16, 150, 318, 150, 16, 1},
{1, 22, 380, 1554, 1554, 380, 22, 1},
{1, 29, 892, 6562, 12432, 6562, 892, 29, 1},
{1, 37, 1987, 25038, 82538, 82538, 25038, 1987, 37, 1},
{1, 46, 4270, 89023, 480380, 825380, 480380, 89023, 4270, 46, 1}
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MATHEMATICA
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m = 1; e[n_, 0, m_] := 1;
e[n_, k_, m_] := 0 /; k >= n;
e[n_, k_, 1] := 1 /; k >= n;
e[n_, k_, m_] := (k + m - 1)e[n - 1, k, m] + (m*n - k + 1 - m)e[n - 1, k - 1, m];
Table[Table[e[n, k, m], {k, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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A054091, A054090, A008517, A156141
Sequence in context: A118245 A104382 A086629 this_sequence A126770 A056588 A156006
Adjacent sequences: A156181 A156182 A156183 this_sequence A156185 A156186 A156187
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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 05 2009
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