A132051 Sixth column of triangle A035342.

1, 63, 2730, 103950, 3786615, 137162025, 5039703900, 189883593900, 7381251402525, 297032627967075, 12395985005353950, 536910000482705850, 24139951470365605875, 1126381171697414758125, 54517938404202375102000

Offset: 6

Author

Wolfdieter Lang Sep 14 2007

Keywords

• nonn
• easy

Comments

a(n), n >= 6, enumerates unordered n-vertex forests composed of six plane increasing ternary trees. See A001147 (number of increasing ternary trees) and a D. Callan comment there. For a picture of some ternary trees see a W. Lang link under A001764.

Crossrefs

Cf. A035521 (fifth column).

Programs

Mathematica

Drop[With[{nn=20},CoefficientList[Series[(-1+1/Sqrt[1-2x])^6/720,{x,0,nn}],x] Range[0,nn]!],6] (* Harvey P. Dale, May 27 2023 *)

Formula

E.g.f.: ((x*c(x/2)*(1-2*x)^(-1/2))^6)/6!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.

E.g.f.: (-1+(1-2*x)^(-1/2))^6/6!.