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Search: id:A154380
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| A154380 |
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Triangle T(n,k), 0<=k<=n, read by rows given by [1, 1, 1, 2, 1, 3, 1,4,1,...] DELTA [1, 0, 0,0,...] where DELTA is the operator defined in A084938. |
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+0
3
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| 1, 1, 1, 2, 3, 1, 5, 9, 5, 1, 15, 29, 20, 7, 1, 52, 102, 77, 35, 9, 1, 203, 392, 302, 157, 54, 11, 1, 877, 1641, 1235, 683, 277, 77, 13, 1, 4140, 7451, 5324, 2987, 1329, 445, 104, 15, 1, 21147, 36525, 24329, 13391, 6230, 2340, 669, 135, 17, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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First column is A000110. Row sums are A154381.
In general, the triangle [r_0,r_1,r_2,....] DELTA [s_0,s_1,s_2,.....] has generating function
1/(1-(r_0*x+s_0*x*y)/(1-(r_1*x+s_1*x*y)/(1-(r_2*x+s_2*x*y)/(1-..... (continued fraction)
A130167*A007318 as infinite lower triangular matrices . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 11 2009]
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FORMULA
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G.f. : 1/(1-(x+xy)/(1-x/(1-x/(1-2x/(1-x/(1-3x/(1-x/(1-4x/(1-... (continued fraction).
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EXAMPLE
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Triangle begins
1,
1, 1,
2, 3, 1,
5, 9, 5, 1,
15, 29, 20, 7, 1,
52, 102, 77, 35, 9, 1,
203, 392, 302, 157, 54, 11, 1
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CROSSREFS
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Sequence in context: A147703 A147747 A039599 this_sequence A155083 A011357 A080409
Adjacent sequences: A154377 A154378 A154379 this_sequence A154381 A154382 A154383
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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), Jan 08 2009
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