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A157012
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Riordan's general Eulerian recursion:m=2: ( 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
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1, 1, 0, 1, 1, 0, 1, 5, 1, 0, 1, 18, 14, 1, 0, 1, 58, 110, 33, 1, 0, 1, 179, 672, 495, 72, 1, 0, 1, 543, 3583, 5163, 1917, 151, 1, 0, 1, 1636, 17590, 43730, 32154, 6808, 310, 1, 0, 1, 4916, 81812, 324190, 411574, 176272, 22904, 629, 1, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Row sums are:
{1, 1, 2, 7, 34, 203, 1420, 11359, 102230, 1022299,...}.
This recursion set doesn't seem to produce the Eulerian 2nd A008517.
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REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, pp. 214-215
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FORMULA
| m=2;
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
| {1},
{1, 0},
{1, 1, 0},
{1, 5, 1, 0},
{1, 18, 14, 1, 0},
{1, 58, 110, 33, 1, 0},
{1, 179, 672, 495, 72, 1, 0},
{1, 543, 3583, 5163, 1917, 151, 1, 0},
{1, 1636, 17590, 43730, 32154, 6808, 310, 1, 0},
{1, 4916, 81812, 324190, 411574, 176272, 22904, 629, 1, 0}
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MATHEMATICA
| 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
| A008517, A008292
Sequence in context: A007912 A019755 A085475 * A102365 A102259 A021200
Adjacent sequences: A157009 A157010 A157011 * A157013 A157014 A157015
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 21 2009
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