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Sixth column of triangle A035342.
1

%I #8 May 27 2023 19:07:32

%S 1,63,2730,103950,3786615,137162025,5039703900,189883593900,

%T 7381251402525,297032627967075,12395985005353950,536910000482705850,

%U 24139951470365605875,1126381171697414758125,54517938404202375102000

%N Sixth column of triangle A035342.

%C 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.

%F 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.

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

%t 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 *)

%Y Cf. A035521 (fifth column).

%K nonn,easy

%O 6,2

%A _Wolfdieter Lang_ Sep 14 2007