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A156003
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Triangle read by rows: t0(n,m)=Binomial[3*n, m - 1]; t(n,m)=t0(n,m)+t0(n,n-m+1)
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0
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2, 7, 7, 37, 18, 37, 221, 78, 78, 221, 1366, 470, 210, 470, 1366, 8569, 3078, 969, 969, 3078, 8569, 54265, 20370, 6195, 2660, 6195, 20370, 54265, 346105, 134620, 42780, 12650, 12650, 42780, 134620, 346105, 2220076, 888057, 296361, 83655, 35100
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are:
{2, 14, 92, 598, 3882, 25232, 164320, 1072310, 7011398, 45928174,...}
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REFERENCES
| B. Brainerd and T. V. Narayana,A Note on Simple Binomial Sampling Plans, Ann. Math. Statist. Volume 32, Number 3 (1961), 906-908. http://www.projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoms/1177704987
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FORMULA
| t0(n,m)=Binomial[3*n, m - 1]; t(n,m)=t0(n,m)+t0(n,n-m+1)
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EXAMPLE
| {2},
{7, 7},
{37, 18, 37},
{221, 78, 78, 221},
{1366, 470, 210, 470, 1366},
{8569, 3078, 969, 969, 3078, 8569},
{54265, 20370, 6195, 2660, 6195, 20370, 54265},
{346105, 134620, 42780, 12650, 12650, 42780, 134620, 346105},
{2220076, 888057, 296361, 83655, 35100, 83655, 296361, 888057, 2220076},
{14307151, 5852955, 2036235, 597835, 169911, 169911, 597835, 2036235, 5852955, 14307151}
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MATHEMATICA
| a[n_, m_] = Binomial[3*n, m - 1];
Table[Table[a[n, m] + a[n, n - m + 1], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A090521 A090523 A164314 * A011416 A086658 A175577
Adjacent sequences: A156000 A156001 A156002 * A156004 A156005 A156006
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 01 2009
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