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 A193618 G.f. A(x) satisfies: A(x)^2 + A(-x)^2 = 2 and A(x)^-2 - A(-x)^-2 = -8*x. 10
 1, 2, -2, -28, 54, 860, -2004, -33720, 86054, 1492908, -4019452, -71101832, 198310460, 3555617432, -10168382696, -184127171952, 536496907782, 9788598556876, -28937139277804, -531135371147368, 1588378827366868, 29295861148032584 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The unsigned version of this sequence, A246062, has g.f.: sqrt( (1 + sqrt(1+8*x)) / (1 + sqrt(1-8*x)) ). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA G.f.: ( 2*(sqrt(1+64*x^2) + 8*x)/(sqrt(1+64*x^2) + 1) )^(1/4). G.f. A(x) = 1/G(x) where G(x) is the g.f. of A193619. EXAMPLE G.f.: A(x) = 1 + 2*x - 2*x^2 - 28*x^3 + 54*x^4 + 860*x^5 - 2004*x^6 +... where A(x)^2 = 1 + 4*x - 64*x^3 + 2048*x^5 - 81920*x^7 + 3670016*x^9 +... and A(x)^-2 = 1 - 4*x + 16*x^2 - 256*x^4 + 8192*x^6 - 327680*x^8 +... PROG (PARI) {a(n)=local(Ox=x*O(x^n), A=(2*(sqrt(1+64*x^2+Ox)+8*x)/(sqrt(1+64*x^2+Ox)+1))^(1/4)); polcoeff(A, n)} (PARI) N=40; x='x+O('x^N); Vec(sqrt(2/(1-8*x+sqrt(1+64*x^2)))) \\ Seiichi Manyama, Aug 26 2020 CROSSREFS Cf. A193619, A246062. Sequence in context: A024577 A121222 A125067 * A246062 A178955 A012000 Adjacent sequences:  A193615 A193616 A193617 * A193619 A193620 A193621 KEYWORD sign AUTHOR Paul D. Hanna, Aug 01 2011 STATUS approved

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Last modified December 6 19:30 EST 2021. Contains 349567 sequences. (Running on oeis4.)