A238111 Twice the large Schroeder numbers A006318.

2, 4, 12, 44, 180, 788, 3612, 17116, 83172, 412196, 2075436, 10586892, 54595476, 284157492, 1490774076, 7875206076, 41854313412, 223636052036, 1200637707852, 6473448634348, 35037238641780, 190299310403924, 1036863750837852, 5665846701859484, 31042935297750180, 170499885177942628

Offset: 0

Author

N. J. A. Sloane, Mar 04 2014

Keywords

• nonn

Comments

Although this is simply twice A006318, it seems to arise often enough to warrant its own entry. See also A001003.

Links

• Li Guo and Jun Pei, Averaging algebras, Schroeder numbers and rooted trees, arXiv preprint arXiv:1401.7386, 2014

Crossrefs

Cf. A006318, A001003.

Programs

Mathematica

Table[-2 I Sqrt[2] LegendreP[n, -1, 2, 3], {n, 0, 25}] (* Jean-François Alcover, Feb 15 2019 *)

Formula

G.f.: (1-x-sqrt(x^2-6*x+1))/x.