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A157637
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A version of my general recursion with third term function:m=2; t(n,m)=If[n*m*(n - m) == 0, 1, n*m*(n - m)/2].
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0
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1, 1, 1, 1, 5, 1, 1, 16, 16, 1, 1, 42, 136, 42, 1, 1, 99, 816, 816, 99, 1, 1, 219, 3951, 10200, 3951, 219, 1, 1, 466, 16632, 94827, 94827, 16632, 466, 1, 1, 968, 63670, 716160, 1601070, 716160, 63670, 968, 1, 1, 1981, 228112, 4657522, 20836740, 20836740
(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, 7, 34, 222, 1832, 18542, 223852, 3162668, 51448712, 951473652,...}.
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FORMULA
| m=2; t(n,m)=If[n*m*(n - m) == 0, 1, n*m*(n - m)/2].
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EXAMPLE
| {1},
{1, 1},
{1, 5, 1},
{1, 16, 16, 1},
{1, 42, 136, 42, 1},
{1, 99, 816, 816, 99, 1},
{1, 219, 3951, 10200, 3951, 219, 1},
{1, 466, 16632, 94827, 94827, 16632, 466, 1},
{1, 968, 63670, 716160, 1601070, 716160, 63670, 968, 1},
{1, 1981, 228112, 4657522, 20836740, 20836740, 4657522, 228112, 1981, 1},
{1, 4017, 779605, 27140334, 222725554, 450174630, 222725554, 27140334, 779605, 4017, 1}
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MATHEMATICA
| f[n_, k_] := If[n*k*(n - k) == 0, 1, n*k*(n - k)/2];
A[n_, 0, m_] := 1; A[n_, n_, m_] := 1;
A[n_, k_, m_] := (m*(n - k) + 1)*A[n - 1, k - 1, m] + (m*k + 1)*A[n - 1, k, m] + m*f[n, k]*A[n - 2, k - 1, m];
Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];
Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]
Table[Table[Sum[A[n, k, m], {k, 0, n}], {n, 0, 10}], {m, 0, 10}];
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CROSSREFS
| A157523
Sequence in context: A174044 A174159 A074060 * A157181 A029847 A154334
Adjacent sequences: A157634 A157635 A157636 * A157638 A157639 A157640
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 03 2009
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