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 A355795 Row 2 of A355793. 4
 1, 3, 33, 507, 9609, 212835, 5350785, 149961675, 4628365305, 155913036915, 5692874399025, 224034935130075, 9456933847187625, 426402330032719875, 20460268520575152225, 1041301103429870128875, 56040353252589013121625, 3180443637298592493577875, 189863589771186976073108625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..18. A. N. Stokes, Continued fraction solutions of the Riccati equation, Bull. Austral. Math. Soc. Vol. 25 (1982), 207-214. FORMULA O.g.f.: A(x) = ( Sum_{k >= 0} t(k+2)/t(2)*x^k )/( Sum_{k >= 0} t(k+1)/t(1)*x^k ), where t(n) = Product_{k = 1..n} 3*k-1 = A008544(n) (triple factorial numbers). A(x)/(1 - 5*x*A(x)) = Sum_{k >= 0} t(k+2)/t(2)*x^k. A(x) = 1/(1 + 5*x - 8*x/(1 + 8*x - 11*x/(1 + 11*x - 14*x/(1 + 14*x - ... )))) (continued fraction). A(x) satisfies the Riccati differential equation 3*x^2*A(x)' + 5*x*A(x)^2 - (1 + 2*x)*A(x) + 1 = 0 with A(0) = 1. Hence by Stokes, A(x) = 1/(1 - 3*x/(1 - 8*x/(1 - 6*x/(1 - 11*x/(1 - 9*x/(1 - 14*x/(1 - 12*x/(1 - ... )))))))), a continued fraction of Stieltjes type. MAPLE n := 2: seq(coeff(series( hypergeom([n+2/3, 1], [], 3*x)/hypergeom([n-1/3, 1], [], 3*x ), x, 21), x, k), k = 0..20); CROSSREFS Cf. A355793 (table). Cf. A112936 (row 0), A355794 (row 1), A355796 (row 3), A355797 (row 4). Cf. A008544, A111528, A355721. Sequence in context: A243251 A336539 A221147 * A291818 A209245 A092170 Adjacent sequences: A355792 A355793 A355794 * A355796 A355797 A355798 KEYWORD nonn,easy AUTHOR Peter Bala, Jul 21 2022 STATUS approved

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Last modified June 21 11:00 EDT 2024. Contains 373544 sequences. (Running on oeis4.)