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 A276316 G.f. A(x) satisfies: x = A(x)-4*A(x)^2+A(x)^3. 4
 1, 4, 31, 300, 3251, 37744, 459060, 5773548, 74474455, 979872036, 13099102575, 177414673488, 2429310288468, 33574008073120, 467717206216760, 6560977611629676, 92595131510426943, 1313820730347196300, 18730821529411507725, 268185082351558093260 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..844 Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019. Thomas M. Richardson, The three 'R's and the Riordan dual, arXiv:1609.01193 [math.CO], 2016. FORMULA G.f.: Series_Reversion(x-4*x^2+x^3). From Robert Israel, Sep 02 2016: (Start) G.f. g(x) satisfies the differential equation (12-184*t-27*t^2)*g''(t) - (92+27*t)*g'(t) + 3*g(t) = 4. (-27*n^2+3)*a(n)+(-184*n^2-276*n-92)*a(n+1)+(12*n^2+36*n+24)*a(n+2) = 0 for n >= 1. (End) a(n) ~ (46 + 13*sqrt(13))^(n - 1/2) / (13^(1/4) * sqrt(Pi) * n^(3/2) * 2^(n + 1/2) * 3^(n - 1/2)). - Vaclav Kotesovec, Aug 22 2017 EXAMPLE G.f.: A(x) = x+4*x^2+31*x^3+300*x^4+3251*x^5+37744*x^6+459060*x^7+... Related Expansions: A(x)^2 = x^2+8*x^3+78*x^4+848*x^5+9863*x^6+120096*x^7+1511634*x^8+... A(x)^3 = x^3+12*x^4+141*x^5+1708*x^6+21324*x^7+272988*x^8+3566761*x^9+... MAPLE S:= series(RootOf(x-4*x^2+x^3-t, x), t, 100): seq(coeff(S, t, j), j=1..100); # Robert Israel, Sep 02 2016 MATHEMATICA Rest[CoefficientList[InverseSeries[Series[x - 4*x^2 + x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 22 2017 *) PROG (PARI) {a(n)=polcoeff(serreverse(x - 4*x^2 + x^3 + x^2*O(x^n)), n)} for(n=1, 30, print1(a(n), ", ")) CROSSREFS Cf. A250886, A276310, A276314, A276315. Sequence in context: A000858 A003436 A307504 * A199683 A114475 A243312 Adjacent sequences: A276313 A276314 A276315 * A276317 A276318 A276319 KEYWORD nonn,easy AUTHOR Tom Richardson, Aug 29 2016 STATUS approved

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Last modified December 10 18:13 EST 2023. Contains 367717 sequences. (Running on oeis4.)