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 A160823 A transform of the large Schroeder numbers. 2
 1, 1, 3, 5, 13, 27, 69, 161, 415, 1033, 2701, 6983, 18521, 49041, 131723, 354493, 962381, 2620675, 7178285, 19724513, 54430023, 150641937, 418294813, 1164528399, 3250685297, 9094701729, 25501672595, 71649158709, 201687341901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Hankel transform is A060656(n+1). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 1/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-x^2/(1-...))))))) (continued fraction); G.f.: (1-x-x^2-sqrt(1-2*x-5*x^2+6*x^3+x^4))/(2*x^2*(1-x)). a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*A006318(k). Conjecture: (n+2)*a(n) -3*(n+1)*a(n-1) +3(2-n)*a(n-2) +(11*n-20)*a(n-3) +(11-5*n)*a(n-4) + (4-n)*a(n-5)=0. - R. J. Mathar, Nov 16 2011 a(n) ~ sqrt((-36 + 63*sqrt(2) + sqrt(8666 - 4936*sqrt(2)))/8) * ((1 + sqrt(13 + 8*sqrt(2)))/2)^n / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, May 01 2018 EXAMPLE G.f. = 1 + x + 3*x^2 + 5*x^3 + 13*x^4 + 27*x^5 + 69*x^6 + 161*x^7 + ... MATHEMATICA CoefficientList[Series[(1-x-x^2-Sqrt[1-2*x-5*x^2+6*x^3+x^4])/(2*x^2*(1- x)), {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2018 *) PROG (PARI) x='x+O('x^50); Vec((1-x-x^2-sqrt(1-2*x-5*x^2+6*x^3+x^4))/(2*x^2*(1-x))) \\ G. C. Greubel, Apr 30 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x-x^2-Sqrt(1-2*x-5*x^2+6*x^3+x^4))/(2*x^2*(1-x)))); // G. C. Greubel, Apr 30 2018 CROSSREFS Sequence in context: A026569 A035082 A005198 * A077443 A147196 A110225 Adjacent sequences:  A160820 A160821 A160822 * A160824 A160825 A160826 KEYWORD easy,nonn AUTHOR Paul Barry, May 27 2009 STATUS approved

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Last modified September 17 12:00 EDT 2021. Contains 347477 sequences. (Running on oeis4.)