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A157011
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Triangle T(n,k) read by rows: T(n,0)=1. T(n,k)= k*T(n-1,k) + (n-k+1)*T(n-1,k-1), 0<k<n, n>=1.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums are apparently in A002627.
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EXAMPLE
| The triangle starts in row n=1 as:
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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MAPLE
| A157011 := proc(n, k) if k <0 or k >= n then 0; elif k =0 then 1; else k*procname(n-1, k)+(n-k+1)*procname(n-1, k-1) ; end if; end proc: # R. J. Mathar, Jun 18 2011
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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, A000096 (column k=1).
Sequence in context: A128718 A112358 A126351 * A092821 A110552 A129161
Adjacent sequences: A157008 A157009 A157010 * A157012 A157013 A157014
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 21 2009
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