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 A282046 From solution to a certain functional equation. 1
 1, 6, 66, 852, 11874, 172860, 2586108, 39403704, 608191266, 9477587436, 148782847572, 2349371691528, 37276209494076, 593819849120712, 9492182832078888, 152184075600182352, 2446292788927524258, 39414680294672271756, 636376864032528135204, 10294159197891381551208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Shaun Cooper, Jesús Guillera, Armin Straub, Wadim Zudilin, Crouching AGM, Hidden Modularity, arXiv:1604.01106 [math.NT], 5-April-2016. See Section 2. MATHEMATICA terms = 20; f[_] = 1; Do[f[z_] = f[z] - f[z/(1+2z)^3]/(1+2z)^2 + f[z^2/(1-4z)^3]/(1-4z)^2 + O[z]^terms // Normal, {terms}]; g[z_] = Sqrt[f[z]] + O[z]^terms; CoefficientList[g[z], z] (* Jean-François Alcover, Oct 10 2018, after Andrey Zabolotskiy *) PROG (Python) fact = [1] for i in range(1, 80):     fact.append(fact[-1]*i) def cnk(n, k):     return fact[n]//fact[k]//fact[n-k] def cc(N): # returns first N terms of A282045     c = [1]     for n in range(1, N):         c.append(sum(cnk(n+k+1, 3*k+1)*4**(n-2*k)*c[k] for k in range(n//2+1)) - sum(cnk(n+2*k+1, 3*k+1)*(-2)**(n-k)*c[k] for k in range(n)))     return c def dd(ccc):     d = [1]     for n in range(1, len(ccc)):         d.append((ccc[n]-sum(d[k]*d[n-k] for k in range(1, n)))//2)     return d print(dd(cc(25))) # Andrey Zabolotskiy, Feb 22 2017 CROSSREFS Cf. A282045. Sequence in context: A173535 A267141 A004355 * A124862 A130977 A191096 Adjacent sequences:  A282043 A282044 A282045 * A282047 A282048 A282049 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 21 2017 EXTENSIONS More terms from Andrey Zabolotskiy, Feb 22 2017 STATUS approved

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Last modified May 11 09:11 EDT 2021. Contains 343788 sequences. (Running on oeis4.)