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A154227
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A recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + n*(n + 1)*A(n - 2, k - 1)/2.
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0
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1, 1, 1, 1, 8, 1, 1, 19, 19, 1, 1, 35, 158, 35, 1, 1, 57, 592, 592, 57, 1, 1, 86, 1629, 5608, 1629, 86, 1, 1, 123, 3767, 28549, 28549, 3767, 123, 1, 1, 169, 7760, 105621, 309458, 105621, 7760, 169, 1, 1, 225, 14694, 320566, 1985274, 1985274, 320566, 14694, 225
(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, 10, 40, 230, 1300, 9040, 64880, 536560, 4641520,...}.
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FORMULA
| A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + n*(n + 1)*A(n - 2, k - 1)/2.
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EXAMPLE
| {1},
{1, 1},
{1, 8, 1},
{1, 19, 19, 1},
{1, 35, 158, 35, 1},
{1, 57, 592, 592, 57, 1},
{1, 86, 1629, 5608, 1629, 86, 1},
{1, 123, 3767, 28549, 28549, 3767, 123, 1},
{1, 169, 7760, 105621, 309458, 105621, 7760, 169, 1},
{1, 225, 14694, 320566, 1985274, 1985274, 320566, 14694, 225, 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*(n + 1)*A[n - 2, k - 1]/2;
Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A051425 A051469 A155494 * A166340 A157178 A174303
Adjacent sequences: A154224 A154225 A154226 * A154228 A154229 A154230
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 05 2009
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