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 A263841 Expansion of (1 - 2*x - x^2)/(sqrt(1+x)*(1-3*x)^(3/2)*2*x) - 1/(2*x). 1
 1, 3, 9, 28, 87, 271, 843, 2619, 8123, 25153, 77763, 240054, 740017, 2278329, 7006093, 21520872, 66039651, 202462113, 620164491, 1898109900, 5805127269, 17741909157, 54188530641, 165405964227, 504601360389, 1538559689751, 4688812503053, 14282580916834, 43486805133903 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..28. A. Asinowski and G. Rote, Point sets with many non-crossing matchings, arXiv preprint arXiv:1502.04925 [cs.CG], 2015. See Table 1. FORMULA D-finite with recurrence: -(n+1)*(n^2+n-3)*a(n) + 2*(n^3+3*n^2-4*n-3)*a(n-1) + 3*(n-1)*(n^2+3*n-1)*a(n-2) = 0. - R. J. Mathar, Feb 17 2016 From Mélika Tebni, Jan 24 2024: (Start) a(n) = A005773(n+1) + A132894(n). E.g.f.: (1+x)*exp(x)*(BesselI(0,2*x) + BesselI(1,2*x)). (End) From Mélika Tebni, Jan 25 2024: (Start) a(n) = Sum_{k=0..n} A189911(k)*binomial(n,k). a(n) = Sum_{k=0..n} (k+1)*binomial(n,k)*binomial(n-k,floor((n-k)/2)). (End) MAPLE A263841 := n -> add((k+1)*binomial(n, k)*binomial(n-k, iquo(n-k, 2)), k = 0 .. n): seq(A263841(n), n = 0 .. 28); # Mélika Tebni, Jan 25 2024 MATHEMATICA CoefficientList[Series[(1-2x-x^2)/(Sqrt[1+x] (1-3x)^(3/2) 2x)-1/(2x), {x, 0, 30}], x] (* Harvey P. Dale, Aug 21 2017 *) PROG (PARI) my(x='x+O('x^40)); Vec((1-2*x-x^2)/(sqrt(1+x)*(1-3*x)^(3/2)*2*x)-1/(2*x)) \\ Altug Alkan, Nov 10 2015 CROSSREFS Cf. A005773, A132894, A189911. Sequence in context: A091140 A052541 A024738 * A052939 A225114 A085839 Adjacent sequences: A263838 A263839 A263840 * A263842 A263843 A263844 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 02 2015 STATUS approved

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Last modified September 11 23:02 EDT 2024. Contains 375842 sequences. (Running on oeis4.)