OFFSET
1,2
LINKS
Emeric Deutsch, Emanuele Munarini, and Simone Rinaldi, Skew Dyck paths, area, and superdiagonal bargraphs, Journal of Statistical Planning and Inference, Vol. 140, Issue 6, June 2010, pp. 1550-1562. Table 1, y_n.
Toufik Mansour and José Luis Ramírez, Enumeration of Fuss-skew paths, Ann. Math. Inform. (2022) Vol. 55, 125-136. See p. 129, eq (2.1) at l=1.
László Németh, Tetrahedron trinomial coefficient transform, arXiv:1905.13475 [math.CO], 2019.
FORMULA
a(n) = hypergeom([3/2, 2, 1-n], [1, 3], -4). - Vladimir Reshetnikov, Apr 25 2016
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
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
a(n) = Sum_{k=1..n} C(2*k,k-1)*C(n-1,k-1). - Vladimir Kruchinin, Sep 17 2020
a(n) ~ 2 * 5^(n - 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Sep 17 2020
MATHEMATICA
Table[HypergeometricPFQ[{3/2, 2, 1-n}, {1, 3}, -4], {n, 1, 20}] (* Vladimir Reshetnikov, Apr 25 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved