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A156046
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A triangle sequence made symmetrical by reverse coefficients: t0(n,m)=(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]); t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2
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0
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2, 2, 2, 2, 4, 2, 2, 7, 7, 2, 2, 22, 25, 22, 2, 2, 100, 118, 118, 100, 2, 2, 606, 702, 717, 702, 606, 2, 2, 4326, 4928, 5021, 5021, 4928, 4326, 2, 2, 35289, 39611, 40210, 40288, 40210, 39611, 35289, 2, 2, 322570, 357855, 362174, 362758, 362758, 362174, 357855
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are:
{2, 4, 8, 18, 73, 440, 3337, 28554, 270512, 2810718, 31841200,...}.
When divided by two this sequence is very close to Pascal's triangle,
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FORMULA
| t0(n,m)=(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]);
t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2
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EXAMPLE
| {2},
{2, 2},
{2, 4, 2},
{2, 7, 7, 2},
{2, 22, 25, 22, 2},
{2, 100, 118, 118, 100, 2},
{2, 606, 702, 717, 702, 606, 2},
{2, 4326, 4928, 5021, 5021, 4928, 4326, 2},
{2, 35289, 39611, 40210, 40288, 40210, 39611, 35289, 2},
{2, 322570, 357855, 362174, 362758, 362758, 362174, 357855, 322570, 2},
{2, 3265934, 3588500, 3623782, 3628086, 3628592, 3628086, 3623782, 3588500, 3265934, 2}
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MATHEMATICA
| Clear[t];
t[n_, m_] =(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[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: A081755 A097859 A028326 * A048003 A098219 A173439
Adjacent sequences: A156043 A156044 A156045 * A156047 A156048 A156049
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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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