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A168441
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Expansion of 1/(1-x/(1-2x/(1-4x/(1-6x/(1-8x/(1-.... (continued fraction).
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2
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1, 1, 3, 17, 155, 2025, 34819, 743329, 18937707, 560071193, 18844479635, 710440531665, 29654234779771, 1357326276747721, 67589738142784803, 3637403230889380097, 210358430818676801675, 13009719599952748481145
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: 1/(1-x-2x^2/(1-6x-24x^2/(1-14x-80x^2/(1-22x-168x^2/(1-30x-288x^2/(1-... (continued fraction).
a(n) = upper left term of M^n, M = an infinite square production matrix as follows:
1, 1, 0, 0, 0, 0, ...
2, 2, 2, 0, 0, 0, ...
4, 4, 4, 4, 0, 0, ...
6, 6, 6, 6, 6, 0, ...
8, 8, 8, 8, 8, 8, ...
...
(where the series (1,2,4,6,8,...) = A004277, positive even integers prefaced with a 1). - Gary W. Adamson, Jul 19 2011
G.f. A(x) = 1 + x/(G(0)-x) where G(k) = 1 - x*(2*k+2)/G(k+1)); (continued fraction, 1-step).- Sergei N. Gladkovskii, Oct 28 2012
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MATHEMATICA
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nmax = 20; CoefficientList[1 + x*Series[1/(1 - x + ContinuedFractionK[-2*k*x, 1, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 23 2024 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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