A217214 G.f.: (P-Q*(sqrt(1-4*x)))/(x*(1-4*x)^3) where P=(1-4*x)^3*(1-x-x^2), Q=1-11*x+39*x^2-40*x^3-22*x^4.

0, 0, 0, 2, 38, 322, 2112, 12210, 65494, 334334, 1647776, 7910916, 37216060, 172263652, 786879680, 3554999370, 15912092070, 70656410550, 311584194240, 1365760098780, 5954667085620, 25839361664220, 111651277670400, 480603648082740, 2061623609421948, 8815899506583852, 37590408710959552

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Luca Ferrari and Emanuele Munarini, Enumeration of saturated chains in Dyck lattices, arXiv preprint arXiv:1203.6807, 2012

Formula

Conjecture D-finite with recurrence: -(n+1)*(423*n-1718)*a(n) +(-423*n^2+4779*n+1718)*a(n-1) +(17801*n^2-84527*n+75390)*a(n-2) -2*(9341*n-20828)*(2*n-7)*a(n-3)=0. - R. J. Mathar, Jan 25 2020

Mathematica

gf = (P-Q(Sqrt[1 - 4x]))/(x (1 - 4x)^3) /. P -> (1 - 4x)^3 (1 - x - x^2) /. Q -> 1 - 11x + 39x^2 - 40x^3 - 22x^4;
CoefficientList[gf + O[x]^27, x] (* Jean-François Alcover, Oct 08 2018 *)

Crossrefs

Cf. A217215.

Sequence in context: A098456 A214909 A226402 * A303618 A179503 A126731

Adjacent sequences: A217211 A217212 A217213 * A217215 A217216 A217217

Keyword

nonn

Author

N. J. A. Sloane, Oct 03 2012

Status

approved