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 A158101 G.f. satisfies: A(x^2) = -4*x + 1/AGM(1, 1 - 8*x/(A(x^2) + 4*x) ). 2
 1, 4, 4, -16, -28, 176, 336, -2496, -4956, 40112, 81488, -694720, -1432688, 12647488, 26360896, -238598400, -501256668, 4623092400, 9772018896, -91458048960, -194263943664, 1839634167360, 3923099632704, -37510172125440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See A060691 for the expansion of AGM(1,1-8x), where AGM denotes the arithmetic-geometric mean. LINKS FORMULA A bisection of A158100. G.f. satisfies: A(x^2) = -4*x + x/Series_Reversion( x/AGM(1,1-8*x) ). From Paul D. Hanna, Feb 04 2010: (Start) G.f. satisfies: A(x) = Sum_{n>=0} C(2n,n)^2*x^n/A(x)^(2n). G.f.: A(x) = [x/Series_Reversion(x*G(x)^2)]^(1/2) where G(x) = Sum_{n>=0} C(2n,n)^2*x^n = 1/AGM(1, (1-16*x)^(1/2)) = g.f. of A002894. (End) EXAMPLE G.f.: A(x) = 1 + 4*x + 4*x^2 - 16*x^3 - 28*x^4 + 176*x^5 + 336*x^6 - ... PROG (PARI) {a(n)=polcoeff(-4*x+x/serreverse(x/agm(1, 1-8*x +O(x^(2*n+1)))), 2*n)} (PARI) {a(n)=local(G=sum(m=0, n, binomial(2*m, m)^2*x^m)+x*O(x^n)); polcoeff((x/serreverse(x*G^2))^(1/2), n)} \\ Paul D. Hanna, Feb 04 2010 CROSSREFS Cf. A060691, A158100. Cf. A002894. - Paul D. Hanna, Feb 04 2010 Sequence in context: A092959 A183433 A322039 * A038234 A099462 A218051 Adjacent sequences:  A158098 A158099 A158100 * A158102 A158103 A158104 KEYWORD sign AUTHOR Paul D. Hanna, Mar 13 2009 STATUS approved

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Last modified September 21 04:59 EDT 2019. Contains 327253 sequences. (Running on oeis4.)