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Search: id:A116089
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| A116089 |
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Riordan array (1,x(1+x)^3). |
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+0
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; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are A099234. Diagonal sums are A116090.
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FORMULA
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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
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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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CROSSREFS
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Sequence in context: A036874 A049403 A104556 this_sequence A122016 A067882 A110033
Adjacent sequences: A116086 A116087 A116088 this_sequence A116090 A116091 A116092
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 04 2006
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