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A116089
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Riordan array (1,x(1+x)^3).
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2
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1, 0, 1, 0, 3, 1, 0, 3, 6, 1, 0, 1, 15, 9, 1, 0, 0, 20, 36, 12, 1, 0, 0, 15, 84, 66, 15, 1, 0, 0, 6, 126, 220, 105, 18, 1, 0, 0, 1, 126, 495, 455, 153, 21, 1, 0, 0, 0, 84, 792, 1365, 816, 210, 24, 1, 0, 0, 0, 36, 924, 3003, 3060, 1330, 276, 27, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are A099234. Diagonal sums are A116090.
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FORMULA
| G.f.: 1/(1-xy(1+x)^3); Number triangle T(n,k)=C(3k,n-k)=C(n,k)C(4k,n)/C(4k,k).
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EXAMPLE
| Triangle begins
1,
0, 1,
0, 3, 1,
0, 3, 6, 1,
0, 1, 15, 9, 1,
0, 0, 20, 36, 12, 1,
0, 0, 15, 84, 66, 15, 1,
0, 0, 6, 126, 220, 105, 18, 1,
0, 0, 1, 126, 495, 455, 153, 21, 1,
0, 0, 0, 84, 792, 1365, 816, 210, 24, 1,
0, 0, 0, 36, 924, 3003, 3060, 1330, 276, 27, 1
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MATHEMATICA
| Join[{1}, Flatten[Table[Binomial[3k, n-k], {n, 20}, {k, 0, n}]]] (* From Harvey P. Dale, Feb 05 2012 *)
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CROSSREFS
| Sequence in context: A036874 A049403 A104556 * A122016 A067882 A110033
Adjacent sequences: A116086 A116087 A116088 * A116090 A116091 A116092
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KEYWORD
| easy,nonn,tabl,changed
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 04 2006
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