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A156233
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A symmetrical recursion triangular sequence: m=4;e(n,k,m)= (2* k + m - 1)e)n - 1, k, m) + (m*n - 2*k + 1 - m)e(n - 1, k - 1, m); t(n,k)=e(n, k, m) + e(n, n - k, m).
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0
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2, 1, 1, 1, 6, 1, 1, 37, 37, 1, 1, 226, 606, 226, 1, 1, 1565, 7972, 7972, 1565, 1, 1, 13514, 102407, 187824, 102407, 13514, 1, 1, 150753, 1445555, 3859373, 3859373, 1445555, 150753, 1, 1, 2105142, 23789060, 79955452, 115641606, 79955452, 23789060
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are:
{2, 2, 8, 76, 1060, 19076, 419668, 10911364, 327340916, 11129591140,
422924463316,...}.
Since m=2 is A060187, this recursion seems to be a MacMahon numbers level recursion.
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FORMULA
| m=4;e(n,k,m)= (2*k + m - 1)e)n - 1, k, m) + (m*n - 2*k + 1 - m)e(n - 1, k - 1, m);
t(n,k)=e(n, k, m) + e(n, n - k, m).
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EXAMPLE
| {2},
{1, 1},
{1, 6, 1},
{1, 37, 37, 1},
{1, 226, 606, 226, 1},
{1, 1565, 7972, 7972, 1565, 1},
{1, 13514, 102407, 187824, 102407, 13514, 1},
{1, 150753, 1445555, 3859373, 3859373, 1445555, 150753, 1},
{1, 2105142, 23789060, 79955452, 115641606, 79955452, 23789060, 2105142, 1},
{1, 34850041, 457127618, 1813119912, 3259697998, 3259697998, 1813119912, 457127618, 34850041, 1},
{1, 656682190, 9977604269, 46096675274, 96031672538, 117399194772, 96031672538, 46096675274, 9977604269, 656682190, 1}
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MATHEMATICA
| Clear[e, n, k, m]; m = 4; e[n_, 0, m_] := 1;
e[n_, k_, m_] := 0 /; k >= n; e[n_, k_, 1] := 1 /; k >= n;
e[n_, k_, m_] := (2*k + m - 1)e[n - 1, k, m] + (m*n - 2*k + 1 - m)e[n - 1, k - 1, m];
Table[Table[e[n, k, m], {k, 0, n - 1}], {n, 1, 10}];
Flatten[%];
Table[Table[e[n, k, m] + e[n, n - k, m], {k, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| A060187
Sequence in context: A112734 A157118 A156186 * A060185 A129110 A112624
Adjacent sequences: A156230 A156231 A156232 * A156234 A156235 A156236
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Feb 06 2009
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