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A156045
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A triangle sequence made symmetrical by reverse coefficients: t0(n,m)=2 + n! - m! - (n - m)!; t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2
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0
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1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 19, 22, 19, 1, 1, 97, 114, 114, 97, 1, 1, 601, 696, 710, 696, 601, 1, 1, 4321, 4920, 5012, 5012, 4920, 4321, 1, 1, 35281, 39600, 40196, 40274, 40196, 39600, 35281, 1, 1, 322561, 357840, 362156, 362738, 362738, 362156, 357840
(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, 4, 12, 62, 424, 3306, 28508, 270430, 2810592, 31840994},...}.
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FORMULA
| t0(n,m)=2 + n! - m! - (n - m)!;
t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2
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EXAMPLE
| {1},
{1, 1},
{1, 2, 1},
{1, 5, 5, 1},
{1, 19, 22, 19, 1},
{1, 97, 114, 114, 97, 1},
{1, 601, 696, 710, 696, 601, 1},
{1, 4321, 4920, 5012, 5012, 4920, 4321, 1},
{1, 35281, 39600, 40196, 40274, 40196, 39600, 35281, 1},
{1, 322561, 357840, 362156, 362738, 362738, 362156, 357840, 322561, 1},
{1, 3265921, 3588480, 3623756, 3628058, 3628562, 3628058, 3623756, 3588480, 3265921, 1
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MATHEMATICA
| Clear[t];
t[n_, m_] = 2 + n! - m! - (n - m)!;
Table[(Table[t[n, m], {m, 0, n}] + Reverse[Table[t[n, m], {m, 0, n}]])/2, {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A128612 A060854 A091378 * A119687 A086856 A052916
Adjacent sequences: A156042 A156043 A156044 * A156046 A156047 A156048
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 02 2009
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