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A141688
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A triangle sequence recurrence using A088305: a(n) = Sum[k*a(n - k), {k, 1, n}]; A(n,k)= a(n - k + 1)*A(n - 1, k - 1) + a(k )*A(n - 1, k).
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1, 1, 1, 1, 6, 1, 1, 26, 26, 1, 1, 99, 416, 99, 1, 1, 352, 5407, 5407, 352, 1, 1, 1200, 62616, 227094, 62616, 1200, 1, 1, 3977, 673728, 8212854, 8212854, 673728, 3977, 1, 1, 12918, 6889153, 269486766, 903413940, 269486766, 6889153, 12918, 1, 1, 41338
(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, 54, 616, 11520, 354728, 17781120, 1456191616, 193636396800}.
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FORMULA
| a(n) = Sum[k*a(n - k), {k, 1, n}]; A(n,k)= a(n - k + 1)*A(n - 1, k - 1) + a(k )*A(n - 1, k).
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EXAMPLE
| {1},
{1, 1},
{1, 6, 1},
{1, 26, 26, 1},
{1, 99, 416, 99, 1},
{1, 352, 5407, 5407, 352, 1},
{1, 1200, 62616, 227094, 62616, 1200, 1},
{1, 3977, 673728, 8212854, 8212854, 673728, 3977, 1},
{1, 12918, 6889153, 269486766, 903413940,269486766, 6889153, 12918, 1},
{1, 41338, 67863290, 8256432767, 88493861004,88493861004, 8256432767, 67863290, 41338, 1}
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MATHEMATICA
| a[0] = 1; a[n_] := a[n] = Sum[k*a[n - k], {k, 1, n}]; A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := a[(n - k + 1)]*A[n - 1, k - 1] + a[k ]*A[n - 1, k]; Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]
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CROSSREFS
| Cf. A088305.
Sequence in context: A169660 A035348 A140945 * A166960 A155908 A105373
Adjacent sequences: A141685 A141686 A141687 * A141689 A141690 A141691
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 09 2008
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