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A144690
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Limit of the coefficient of x^(2^m+n) in B(x)^(n+1) as m grows, where B(x) = Sum_{k>=0} x^(2^k).
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4
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1, 2, 6, 16, 130, 636, 5712, 34336, 811458, 7151380, 113034746, 1049982792, 25276020640, 293841338896, 5712436923000, 68827002466176, 3739997267623490, 60752008945662372, 1718332635327516238, 26832922324005759560, 1099199814287516279394
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The g.f. of A144691(n) = a(n)/(n+1) appears to have an interesting functional interpretation.
For a fixed n, the sequence of [x^(2^m+n)] B(x)^(n+1), m=0,1,2,... seems to stabilize at m = n + A023416(n). [From Max Alekseyev (maxale(AT)gmail.com), Dec 19 2011]
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LINKS
| Max Alekseyev, Table of n, a(n) for n = 0..27
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FORMULA
| a(n) = (n+1)*A144691(n).
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PROG
| (PARI) { a(n) = local(m=n+log(n+.5)\log(2), 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
| Cf. A007178, A144691, A144692, A135068, A135069, A135070, A135071.
Sequence in context: A147941 A147932 A147923 * A118305 A139629 A057497
Adjacent sequences: A144687 A144688 A144689 * A144691 A144692 A144693
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 10 2008
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EXTENSIONS
| a(14), a(15) corrected and a(16)-a(23) added by Max Alekseyev (maxale(AT)gmail.com), May 03 2011
a(24)-a(27) in b-file from Max Alekseyev (maxale(AT)gmail.com), Dec 19 2011
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