OFFSET
0,2
LINKS
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)
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 02 2015
STATUS
approved