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Search: id:A073192
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| A073192 |
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Number of general plane trees whose n-th subtree from the left is equal with the n-th subtree from the right, for all its subtrees (i.e. are palindromic in the shallow sense). |
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+0
6
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| 1, 1, 2, 3, 8, 18, 54, 155, 500, 1614, 5456, 18630, 64960, 228740, 814914, 2926323, 10589916, 38561814, 141219432, 519711666, 1921142832, 7129756188, 26555149404, 99228108222, 371886574632, 1397548389644, 5265131346368
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OFFSET
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0,3
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COMMENT
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The gatomorphism A057508 fixes only these kinds of trees, so this occurs in the table A073202 as row 168.
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FORMULA
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a(n) = Sum_{i=0..n, (n-i) is even} Gat((n-i)/2)*Gat(i-1), where Gat(-1) = 1, and otherwise like A000108(n).
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MAPLE
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A073192 := proc(n) local d; add( (`mod`((n-d+1), 2))*Cat((n-d)/2)*(`if`((0=d), 1, Cat(d-1))), d=0..n); end;
Cat := n -> binomial(2*n, n)/(n+1);
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CROSSREFS
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Occurs for first time in A073202 as row 168. A073193(n) = (A000108(n)+A073192(n))/2. Cf. also A073190.
Sequence in context: A079224 A002369 A005957 this_sequence A113183 A041205 A002356
Adjacent sequences: A073189 A073190 A073191 this_sequence A073193 A073194 A073195
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Jun 25 2002
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