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Search: id:A127628
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| 1, 6, 42, 300, 2154, 15492, 111492, 802584, 5778090, 41600532, 299517996, 2156509416, 15526797252, 111792690600, 804906480840, 5795323452720, 41726317225770, 300429441596340, 2163091823919900, 15574260559056840
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OFFSET
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0,2
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COMMENT
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Image of 6^n under the Catalan transform g(x)->g(xc(x)). The Hankel transform of this sequence and of the aerated version with g.f. 1/(1-6*x^2*c(x^2)) is 6^n. In general, the expansions of 1/(1-k*x*c(x)) and 1/(1-k*x^2*c(x^2)) have Hankel transform k^n.
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FORMULA
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a(n)=if(n=0,1,sum{k=1..n, C(2n-k-1,n-k)*k*6^k/n}); a(n)=sum{k=0..n, C(2n,n-k)(2k+1)5^k/(n+k+1)};
a(n) = Sum_{k, 0<=k<=n}A106566(n,k)*6^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 04 2007
a(n)= Sum{k, 0<=k<=n}A039599(n,k)*5^k. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 08 2007
a(0)=1, a(n)=(36*a(n-1)-6*A000108(n-1))/5 for n>=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 27 2007
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CROSSREFS
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Sequence in context: A055272 A155196 A147838 this_sequence A111602 A091164 A004982
Adjacent sequences: A127625 A127626 A127627 this_sequence A127629 A127630 A127631
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KEYWORD
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nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 20 2007
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