|
%I #29 Mar 03 2024 14:30:23
%S 1,5,24,114,541,2573,12275,58747,282003,1357407,6549906,31675020,
%T 153481299,745011075,3622111560,17635418730,85975792075,419644943495,
%U 2050493623760,10029194506990,49098707209695,240568930012575
%N a(n) is the number of integer strings s(0),...,s(n) counted by array T in A026386 that have s(n)=2; also a(n) = T(2n,n-1).
%H Emeric Deutsch, Emanuele Munarini, and Simone Rinaldi, <a href="http://dx.doi.org/10.1016/j.jspi.2009.12.013">Skew Dyck paths, area, and superdiagonal bargraphs</a>, Journal of Statistical Planning and Inference, Vol. 140, Issue 6, June 2010, pp. 1550-1562. Table 1, y_n.
%H Toufik Mansour and José Luis Ramírez, <a href="https://doi.org/10.33039/ami.2022.01.001">Enumeration of Fuss-skew paths</a>, Ann. Math. Inform. (2022) Vol. 55, 125-136. See p. 129, eq (2.1) at l=1.
%H László Németh, <a href="https://arxiv.org/abs/1905.13475">Tetrahedron trinomial coefficient transform</a>, arXiv:1905.13475 [math.CO], 2019.
%F a(n) = hypergeom([3/2, 2, 1-n], [1, 3], -4). - _Vladimir Reshetnikov_, Apr 25 2016
%F D-finite with recurrence -(n+1)*(2*n-1)*a(n) +(12*n^2-2*n+1)*a(n-1) -5*(2*n+1)*(n-2)*a(n-2)=0. - _R. J. Mathar_, Jun 21 2018
%F G.f.: ((x-1)*sqrt((5*x-1)/(x-1))-3*x+1)/(2*x*sqrt((5*x-1)/(x-1))). - _Vladimir Kruchinin_, Sep 17 2020
%F a(n) = Sum_{k=1..n} C(2*k,k-1)*C(n-1,k-1). - _Vladimir Kruchinin_, Sep 17 2020
%F a(n) ~ 2 * 5^(n - 1/2) / sqrt(Pi*n). - _Vaclav Kotesovec_, Sep 17 2020
%t Table[HypergeometricPFQ[{3/2, 2, 1-n}, {1, 3}, -4], {n, 1, 20}] (* _Vladimir Reshetnikov_, Apr 25 2016 *)
%K nonn
%O 1,2
%A _Clark Kimberling_
|
