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Search: id:A144691
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| A144691 |
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a(n) = Limit_{m->infinity} [x^(2^m+n)] B(x)^(n+1)/(n+1) for n>=0, where B(x) = Sum_{k>=0} x^(2^k); thus a(n) = A144690(n)/(n+1). |
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+0
3
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| 1, 1, 2, 4, 26, 106, 816, 4292, 90162, 715138, 10275886, 87498566, 1944309280, 20988667064, 351769697800, 3865796198136
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = limit, as m grows, of coefficient of x^(2^m+n) in B(x)^(n+1)/(n+1)
where B(x) = x + x^2 + x^4 + x^8 +...+ x^(2^k) +...
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FORMULA
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Given g.f. A(x), let G(x) = g.f. of A144692 where
A(x/G(x)) = G(x) = x/Series_Reversion[x/*A(x)] and G(x*A(x)) = A(x).
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EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 26*x^4 + 106*x^5 + 816*x^6 +...
A(x/G(x)) = G(x) = x/Series_Reversion[x/*A(x)] where
G(x) = 1 + x + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...
and G(x) appears to continue with only even powers of x (cf. A144692).
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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)/(n+1), 2^m+n))}
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CROSSREFS
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Cf. A007178, A144690, A144692.
Sequence in context: A129894 A028386 A155120 this_sequence A085700 A087404 A009237
Adjacent sequences: A144688 A144689 A144690 this_sequence A144692 A144693 A144694
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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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