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Search: id:A154919
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| A154919 |
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A triangular sequence based on: t0(n,m)=Binomial[3*n, 2*m]; by coefficient reversal. t(n,m)=t0(n,m)+reverse(t0(n,m)). |
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+0
1
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| 2, 4, 4, 16, 30, 16, 85, 162, 162, 85, 496, 990, 990, 990, 496, 3004, 6540, 6370, 6370, 6540, 3004, 18565, 43911, 46818, 37128, 46818, 43911, 18565, 116281, 294140, 358701, 257754, 257754, 358701, 294140, 116281, 735472, 1961532, 2714782
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are:
{2, 8, 62, 494, 3962, 31828, 255716, 2053752, 16486218, 132274304, 1060792742}
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FORMULA
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t0(n,m)=Binomial[3*n, 2*m];
Coefficient reversal applied:
t(n,m)=t0(n,m)+reverse(t0(n,m)).
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EXAMPLE
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{2},
{4, 4},
{16, 30, 16},
{85, 162, 162, 85},
{496, 990, 990, 990, 496},
{3004, 6540, 6370, 6370, 6540, 3004},
{18565, 43911, 46818, 37128, 46818, 43911, 18565}, {116281, 294140, 358701, 257754, 257754, 358701, 294140, 116281},
{735472, 1961532, 2714782, 2095852, 1470942, 2095852, 2714782, 1961532, 735472},
{4686826, 13038246, 20075850, 17679870, 10656360, 10656360, 17679870, 20075850, 13038246, 4686826},
{30045016, 86493660, 145450080, 146016450, 92346150, 60090030, 92346150, 146016450, 145450080, 86493660, 30045016}
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MATHEMATICA
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Clear[t, p, q, n, m, a];
t[n_, m_] = Binomial[3*n, 2*m];
Table[Table[t[n, m], {m, 0, n}] + Reverse[Table[t[n, m], {m, 0, n}]], {n, 0, 10}]
Flatten[%]
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CROSSREFS
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Sequence in context: A071337 A087481 A038210 this_sequence A019230 A088042 A013140
Adjacent sequences: A154916 A154917 A154918 this_sequence A154920 A154921 A154922
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KEYWORD
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nonn,tabl,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 17 2009
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