A026388 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).

1, 5, 24, 114, 541, 2573, 12275, 58747, 282003, 1357407, 6549906, 31675020, 153481299, 745011075, 3622111560, 17635418730, 85975792075, 419644943495, 2050493623760, 10029194506990, 49098707209695, 240568930012575

Offset

1,2

Links

Table of n, a(n) for n=1..22.

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

Sequence in context: A141223 A289783 A140766 * A242509 A057969 A004254

Adjacent sequences: A026385 A026386 A026387 * A026389 A026390 A026391

Keyword

nonn

Author

Clark Kimberling

Status

approved