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A317798
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G.f.: Sum_{n>=0} (3*(1+x)^n - 1)^n / 3^(n+1).
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1
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1, 15, 786, 69261, 8554530, 1359020643, 263929299177, 60582032629791, 16046282916588207, 4817035600778756553, 1616224504900354928832, 599373591433178971787007, 243449152911402772344286998, 107482020677618238226506065235, 51249638236281451846248205583562, 26247197050200652206165329786055981, 14369481728948627418149559363836673273
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..16.
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FORMULA
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G.f. satisfies:
(1) Sum_{n>=0} 3^n * (1+x)^(n^2) / (3 + (1+x)^n)^(n+1).
(2) Sum_{n>=0} ((1+x)^n - 1/3)^n / 3.
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EXAMPLE
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G.f.: A(x) = 1 + 15*x + 786*x^2 + 69261*x^3 + 8554530*x^4 + 1359020643*x^5 + 263929299177*x^6 + 60582032629791*x^7 + 16046282916588207*x^8 + ...
such that
A(x) = 1/3 + (3*(1+x) - 1)/3^2 + (3*(1+x)^2 - 1)^3/3^3 + (3*(1+x)^3 - 1)^3/3^4 + (3*(1+x)^4 - 1)^4/3^5 + (3*(1+x)^5 - 1)^5/3^6 + ...
Also,
A(x) = 1/4 + 3*(1+x)/(3 + (1+x))^2 + 3^2*(1+x)^4/(3 + (1+x)^2)^3 + 3^3*(1+x)^9/(3 + (1+x)^3)^4 + 3^4*(1+x)^16/(3 + (1+x)^4)^5 + 3^5*(1+x)^25/(3 + (1+x)^5)^6 + 3^6*(1+x)^36/(3 + (1+x)^6)^7 + ...
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CROSSREFS
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Cf. A122400, A301463, A317799, A301582.
Sequence in context: A333562 A116094 A267754 * A280310 A211104 A279493
Adjacent sequences: A317795 A317796 A317797 * A317799 A317800 A317801
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Aug 14 2018
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STATUS
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approved
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