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Search: id:A144690
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| A144690 |
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a(n) = Limit_{m->infinity} [x^(2^m+n)] B(x)^(n+1) for n>=0, where B(x) = Sum_{k>=0} x^(2^k). |
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+0
3
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| 1, 2, 6, 16, 130, 636, 5712, 34336, 811458, 7151380, 113034746, 1049982792, 25276020640, 293841338896, 5276545467000, 61852739170176
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The g.f. of A144691(n) = a(n)/(n+1) appears to have an interesting functional interpretation.
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FORMULA
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a(n) = (n+1)*A144691(n).
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EXAMPLE
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a(n) = limit, as m grows, of coefficient of x^(2^m+n) in B(x)^(n+1)
where B(x) = x + x^2 + x^4 + x^8 +...+ x^(2^k) +...
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PROGRAM
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(PARI) {a(n)=local(m=n+3, B=sum(k=0, m, x^(2^k))); if(n<0, 0, polcoeff((B+O(x^(2^m+n+1)))^(n+1), 2^m+n))}
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CROSSREFS
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Cf. A007178, A144691, A144692.
Adjacent sequences: A144687 A144688 A144689 this_sequence A144691 A144692 A144693
Sequence in context: A147941 A147932 A147923 this_sequence A118305 A139629 A057497
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KEYWORD
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more,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 10 2008
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