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A307397 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} x^k*A(x)^k/(1 + x^k*A(x)^k). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..29.

FORMULA

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)).

EXAMPLE

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 + ...

MATHEMATICA

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]

CROSSREFS

Cf. A048272, A190790, A192206, A307399, A307401.

Sequence in context: A066143 A110045 A108931 * A032100 A340729 A226593

Adjacent sequences:  A307394 A307395 A307396 * A307398 A307399 A307400

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 07 2019

STATUS

approved

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Last modified May 10 00:35 EDT 2021. Contains 343747 sequences. (Running on oeis4.)