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A156049
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Triangle read by rows: t(n,m)=Binomial[n, m] + 2*(1 + n! - m! - (n - m)!).
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1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 40, 48, 40, 1, 1, 197, 236, 236, 197, 1, 1, 1206, 1405, 1438, 1405, 1206, 1, 1, 8647, 9859, 10057, 10057, 9859, 8647, 1, 1, 70568, 79226, 80446, 80616, 80446, 79226, 70568, 1, 1, 645129, 715714, 724394, 725600, 725600
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sum are:(n+1)!+f(n);
{1, 2, 6, 24, 130, 868, 6662, 57128, 541098, 5621676, 63682990,...}.
Sequence designed to be Eulerian numbers like:
the result is slightly larger.
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FORMULA
| t(n,m)=Binomial[n, m] + 2*(1 + n! - m! - (n - m)!).
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EXAMPLE
| {1},
{1, 1},
{1, 4, 1},
{1, 11, 11, 1},
{1, 40, 48, 40, 1},
{1, 197, 236, 236, 197, 1},
{1, 1206, 1405, 1438, 1405, 1206, 1},
{1, 8647, 9859, 10057, 10057, 9859, 8647, 1},
{1, 70568, 79226, 80446, 80616, 80446, 79226, 70568, 1},
{1, 645129, 715714, 724394, 725600, 725600, 724394, 715714, 645129, 1},
{1, 6531850, 7177003, 7247630, 7256324, 7257374, 7256324, 7247630, 7177003, 6531850, 1}
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MATHEMATICA
| Clear[f];
f[n_, m_] = Binomial[n, m] + 2*(1 + n! - m! - (n - m)!);
Table[Table[f[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A157221 A146967 A173152 * A192015 A205946 A101919
Adjacent sequences: A156046 A156047 A156048 * A156050 A156051 A156052
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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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