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 A073190 Number of general plane trees which are either empty (the case a(0)), or whose root degree is either 1 (i.e., the planted trees) or the two leftmost subtrees (of the root node) are identical. 10
 1, 1, 2, 3, 8, 20, 60, 181, 584, 1916, 6476, 22210, 77416, 272840, 971640, 3488925, 12621168, 45946156, 168206604, 618853270, 2286974856, 8485246456, 31596023208, 118037654258, 442287721872, 1661790513944, 6259494791096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The Catalan bijection A072796 fixes only these kinds of trees, so this occurs in the table A073202 as row 1. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(0)=1, a(n) = Cat(n-1) + Sum_{i=0..n-2, (n-i) is even} Cat((n-i-2)/2)*Cat(i), where Cat(n) is A000108(n). MAPLE A073190 := proc(n) local d; Cat(n-1)+ add( (`mod`((n-d+1), 2))*Cat((n-d-2)/2)*Cat(d), d=0..n-2); end; Cat := n -> binomial(2*n, n)/(n+1); MATHEMATICA a[n_] := CatalanNumber[n - 1] + Sum[Mod[n - d + 1, 2]*CatalanNumber[(n - d - 2)/2]*CatalanNumber[d], {d, 0, n - 2}]; a[0] = 1; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 06 2016 *) PROG (PARI) Cat(n) = binomial(2*n, n)/(n+1); a(n) = if (n==0, 1, Cat(n-1) + sum(i=0, n-2, if (!((n-i)%2), Cat((n-i-2)/2)*Cat(i)))); \\ Michel Marcus, May 30 2018 CROSSREFS Occurs for first time in A073202 as row 1. A073191(n) = (A000108(n)+A073190(n))/2. Cf. also A073192. Sequence in context: A167123 A029895 A073268 * A066051 A056971 A108125 Adjacent sequences:  A073187 A073188 A073189 * A073191 A073192 A073193 KEYWORD nonn AUTHOR Antti Karttunen, Jun 25 2002 STATUS approved

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Last modified January 19 17:59 EST 2020. Contains 331051 sequences. (Running on oeis4.)