# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a132051 Showing 1-1 of 1 %I A132051 #8 May 27 2023 19:07:32 %S A132051 1,63,2730,103950,3786615,137162025,5039703900,189883593900, %T A132051 7381251402525,297032627967075,12395985005353950,536910000482705850, %U A132051 24139951470365605875,1126381171697414758125,54517938404202375102000 %N A132051 Sixth column of triangle A035342. %C A132051 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 A132051 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 A132051 E.g.f.: (-1+(1-2*x)^(-1/2))^6/6!. %t A132051 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 A132051 Cf. A035521 (fifth column). %K A132051 nonn,easy %O A132051 6,2 %A A132051 _Wolfdieter Lang_ Sep 14 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE