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 A036370 Triangle of coefficients of generating function of ternary rooted trees of height at most n. 19
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1, 1, 1, 1, 2, 4, 7, 12, 20, 31, 47, 70, 99, 137, 184, 239, 300, 369, 432, 498, 551, 594, 614, 624, 601, 570, 514, 453, 378, 312, 238, 181, 128, 89, 56, 37, 20, 12, 6, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS Alois P. Heinz, Rows n = 0..8, flattened FORMULA T_{i+1}(z) = 1 +z*(T_i(z)^3/6 +T_i(z^2)*T_i(z)/2 +T_i(z^3)/3); T_0(z) = 1. EXAMPLE 1; 1, 1; 1, 1, 1, 1, 1; 1, 1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1; ... MAPLE T:= proc(n) option remember; local f, g;       if n=0 then 1     else f:= z-> add([T(n-1)][i]*z^(i-1), i=1..nops([T(n-1)]));          g:= expand(1 +z*(f(z)^3/6 +f(z^2)*f(z)/2 +f(z^3)/3));          seq(coeff(g, z, i), i=0..degree(g, z))       fi     end: seq(T(n), n=0..5); # Alois P. Heinz, Sep 26 2011 MATHEMATICA T[n_] := T[n] = Module[{f, g}, If[n == 0, {1}, f[z_] = Sum[T[n-1][[i]]*z^(i-1), {i, 1, Length[T[n-1]]}]; g = Expand[1+z*(f[z]^3/6+f[z^2]*f[z]/2+f[z^3]/3)]; Table[Coefficient [g, z, i], {i, 0, Exponent[g, z]}]]]; Table[T[n], {n, 0, 5}] // Flatten (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *) CROSSREFS Cf. A036437. Sequence in context: A319715 A088807 A036371 * A005208 A110007 A327715 Adjacent sequences:  A036367 A036368 A036369 * A036371 A036372 A036373 KEYWORD nonn,easy,tabf AUTHOR N. J. A. Sloane, Eric Rains (rains(AT)caltech.edu) STATUS approved

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Last modified June 18 03:46 EDT 2021. Contains 345098 sequences. (Running on oeis4.)