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A154233
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A recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) +(n^2 - n - 1)*A(n - 2, k - 1).
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0
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1, 1, 1, 1, 7, 1, 1, 19, 19, 1, 1, 39, 171, 39, 1, 1, 69, 761, 761, 69, 1, 1, 111, 2429, 8533, 2429, 111, 1, 1, 167, 6335, 52817, 52817, 6335, 167, 1, 1, 239, 14383, 231611, 711477, 231611, 14383, 239, 1, 1, 329, 29485, 809809, 5643801, 5643801, 809809, 29485, 329
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 9, 40, 251, 1662, 13615, 118640, 1203945, 12966850,...}.
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FORMULA
| A(n,k)= A(n - 1, k - 1) + A(n - 1, k) +(n^2 - n - 1)*A(n - 2, k - 1).
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EXAMPLE
| {1},
{1, 1},
{1, 7, 1},
{1, 19, 19, 1},
{1, 39, 171, 39, 1},
{1, 69, 761, 761, 69, 1},
{1, 111, 2429, 8533, 2429, 111, 1},
{1, 167, 6335, 52817, 52817, 6335, 167, 1},
{1, 239, 14383, 231611, 711477, 231611, 14383, 239, 1},
{1, 329, 29485, 809809, 5643801, 5643801, 809809, 29485, 329, 1}
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MATHEMATICA
| A[n_, 1] := 1; A[n_, n_] := 1;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n^2 - n - 1)*A[n - 2, k - 1];
Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A141597 A176561 A176284 * A174033 A119727 A157272
Adjacent sequences: A154230 A154231 A154232 * A154234 A154235 A154236
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 05 2009
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