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A166960
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A generalized Stirling 2nd ( A008277)numbers recursion ;m=1; A(n,k)= (m*n - m*k + 1)A(n - 1, k - 1) + k*(m*k - (m - 1))A(n - 1, k)
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0
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1, 1, 1, 1, 6, 1, 1, 27, 21, 1, 1, 112, 270, 58, 1, 1, 453, 2878, 1738, 141, 1, 1, 1818, 28167, 39320, 8739, 318, 1, 1, 7279, 264411, 769955, 375755, 37665, 685, 1, 1, 29124, 2430652, 13905746, 13243650, 2858960, 146560, 1434, 1, 1, 116505, 22108860
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Row sums are:
{1, 2, 8, 50, 442, 5212, 78364, 1455752, 32616128, 864550088,..}
The quadratic scale for these sets seems to be:
{1,3*(m+1),1}
compared the general Pascal triangle recursion on which this was based of:
[1,2*(m+1),1}
Pascal: {1,2,1]; Eulerian:[1,4,1]; Macmahon:{1,6,1},etc.
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FORMULA
| m=1;
A(n,k)= (m*n - m*k + 1)A(n - 1, k - 1) + k*(m*k - (m - 1))A(n - 1, k)
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EXAMPLE
| {1},
{1, 1},
{1, 6, 1},
{1, 27, 21, 1},
{1, 112, 270, 58, 1},
{1, 453, 2878, 1738, 141, 1},
{1, 1818, 28167, 39320, 8739, 318, 1},
{1, 7279, 264411, 769955, 375755, 37665, 685, 1},
{1, 29124, 2430652, 13905746, 13243650, 2858960, 146560, 1434, 1},
{1, 116505, 22108860, 239506500, 414525726, 169140810, 18617280, 531456, 2949, 1}
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MATHEMATICA
| A[n_, 1] := 1 A[n_, n_] := 1
A[n_, k_] := (m*n - m*k + 1)A[n - 1, k - 1] + k*(m*k - (m - 1))A[n - 1, k]
Table[Flatten[ Table[A[n, k], {n, 10}, {k, n}]], {m, 0, 4}]
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CROSSREFS
| Cf. A008277
Sequence in context: A035348 A140945 A141688 * A155908 A105373 A201461
Adjacent sequences: A166957 A166958 A166959 * A166961 A166962 A166963
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 25 2009
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