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Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(2*n-1).
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1, 1, 8, 61, 600, 6072, 65804, 733435, 8415694, 98529785, 1173278329, 14162417506, 172914841649, 2131621288494, 26495818020038, 331706510158239, 4178800564364333, 52935845003315662, 673878770026778330, 8616336680850069832, 110606714769468383785, 1424933340070339610543
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(3*n-1).
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1, 2, 34, 677, 15660, 393790, 10433402, 286990626, 8117763488, 234635708480, 6899771599141, 205768408153474, 6208628685564955, 189188990142419693, 5813805339043713267, 179968235623379467274, 5606627898452185950618, 175650401043239524832783, 5530500462355496324862920
Expansion of g.f. A(x) satisfying 1 = Sum_{n=-oo..+oo} x^n * (2*A(x) - (-x)^n)^(4*n-1).
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1, 4, 150, 7003, 380817, 22517717, 1405927141, 91215539609, 6089092570148, 415519886498886, 28855638743197866, 2032628861705203315, 144884697917577076857, 10430845410431559928714, 757390467820895322043476, 55401570124877193188443429, 4078685155312165112343519832
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