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Search: id:A015084
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| A015084 |
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q-Catalan numbers (recurrence version) for q=3. |
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+0
1
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| 1, 1, 4, 43, 1252, 104098, 25511272, 18649337311, 40823535032644, 267924955577741566, 5274102955963545775864, 311441054994969341088610030, 55171471477692117486494217498280
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Limit_{n->inf} a(n)/3^((n-1)(n-2)/2) = Product{k=1..inf} 1/(1-1/3^k) = 1.785312341998534190367486296013703535718796... - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2005
It appears that the Hankel transform is 3^A002412(n). [From Paul Barry (pbarry(AT)wit.ie), Aug 01 2008]
Hankel transform of the aerated sequence is 3^C(n+1,3). [From Paul Barry (pbarry(AT)wit.ie), Oct 31 2008]
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FORMULA
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a(n) = sum_{i=1}^{n-1} q^{(i-1)} a(i) a(n-i).
G.f. satisfies: A(x) = 3*x/(3-A(3*x)) = x/(1-x/(1-3*x/(1-3^2*x/(1-3^3*x/(1-...))))) (continued fraction). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2005
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PROGRAM
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(PARI) a(n)=if(n==1, 1, sum(i=1, n-1, 3^(i-1)*a(i)*a(n-i))) (Hanna)
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CROSSREFS
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Sequence in context: A130545 A027311 A074702 this_sequence A102388 A071125 A053314
Adjacent sequences: A015081 A015082 A015083 this_sequence A015085 A015086 A015087
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KEYWORD
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nonn
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
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More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2005
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