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A307529 G.f. A(x) satisfies: A(x) = (1 - x^2*A(x)^2)/(1 - x^2*A(x)^2 - x^3*A(x)^3). 1
1, 0, 0, 1, 0, 1, 4, 1, 10, 23, 18, 92, 168, 241, 856, 1480, 2904, 8266, 14854, 33496, 83578, 161047, 380488, 884326, 1819714, 4321045, 9730466, 21019404, 49456092, 110408981, 246005440, 572574553, 1281705752, 2906696339, 6711882928, 15128432758, 34625418170 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..36.

FORMULA

G.f. A(x) satisfies: A(x) = Sum_{k>=0} A000931(k)*x^k*A(x)^k.

G.f.: A(x) = (1/x)*Series_Reversion(x*(1 - x^2 - x^3)/(1 - x^2)).

EXAMPLE

G.f.: A(x) = 1 + x^3 + x^5 + 4*x^6 + x^7 + 10*x^8 + 23*x^9 + 18*x^10 + 92*x^11 + 168*x^12 + ...

MATHEMATICA

terms = 37; CoefficientList[1/x InverseSeries[Series[x (1 - x^2 - x^3)/(1 - x^2), {x, 0, terms}], x], x]

terms = 36; A[_] = 0; Do[A[x_] = (1 - x^2 A[x]^2)/(1 - x^2 A[x]^2 - x^3 A[x]^3) + O[x]^(terms + 1) // Normal, {terms + 1}]; CoefficientList[A[x], x]

terms = 37; p[n_] := p[n] = SeriesCoefficient[(1 - x^2)/(1 - x^2 - x^3), {x, 0, n}]; A[_] = 1; Do[A[x_] = Sum[p[k] x^k A[x]^k, {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

CROSSREFS

Cf. A000931, A049124, A049140, A067955, A307411, A307412, A307413, A307528.

Sequence in context: A182971 A062145 A178216 * A019213 A019128 A296419

Adjacent sequences:  A307526 A307527 A307528 * A307530 A307531 A307532

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 12 2019

STATUS

approved

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Last modified February 24 13:05 EST 2020. Contains 332209 sequences. (Running on oeis4.)