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A307397
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G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} x^k*A(x)^k/(1 + x^k*A(x)^k).
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2
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1, 1, 1, 3, 8, 18, 50, 150, 429, 1258, 3835, 11740, 36148, 112856, 355318, 1124582, 3582186, 11477162, 36939043, 119387415, 387393424, 1261422550, 4120343870, 13498085604, 44337516318, 145993301239, 481812344551, 1593439356575, 5280074015618, 17528034861180
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..29.
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FORMULA
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G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} A048272(k)*x^k*A(x)^k.
G.f.: A(x) = (1/x)*Series_Reversion(x/(1 + Sum_{k>=1} A048272(k)*x^k)).
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 8*x^4 + 18 x^5 + 50*x^6 + 150*x^7 + 429*x^8 + 1258*x^9 + 3835*x^10 + ...
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MATHEMATICA
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terms = 30; A[_] = 0; Do[A[x_] = 1 + Sum[x^k A[x]^k/ (1 + x^k A[x]^k), {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 30; A[_] = 0; Do[A[x_] = 1 + Sum[Sum[(-1)^(d + 1), {d, Divisors[k]}] x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 30; CoefficientList[1/x InverseSeries[Series[x/(1 + Sum[Sum[(-1)^(d + 1), {d, Divisors[k]}] x^k, {k, 1, terms}]), {x, 0, terms}], x], x]
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CROSSREFS
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Cf. A048272, A190790, A192206, A307399, A307401.
Sequence in context: A066143 A110045 A108931 * A032100 A340729 A226593
Adjacent sequences: A307394 A307395 A307396 * A307398 A307399 A307400
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Apr 07 2019
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STATUS
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approved
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