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A119365
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Generalized Catalan numbers for triangle A119335.
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5
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1, 0, 0, 1, 6, 20, 51, 126, 392, 1513, 5877, 21054, 71270, 242463, 863590, 3193737, 11889414, 43783908, 159998493, 586908936, 2175907284, 8138471667, 30541703733, 114620380032, 430344635913, 1619584557885, 6116422089050
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OFFSET
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0,5
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COMMENTS
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Counts rooted planar n-trees whose number of leaves is divisible by 3.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} if(mod(n-k,3)=0, (1/n)*C(n,k)*C(n,k+1), 0).
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MAPLE
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local k;
if n = 0 then
return 1
end if;
a := 0 ;
for k from 0 to n do
if modp(n-k, 3) = 0 then
a := a+binomial(n, k)*binomial(n, k+1) ;
end if;
end do:
a/n;
end proc:
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MATHEMATICA
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A119335[n_, k_] := Sum[Binomial[k, 3j] Binomial[n-k, 3j], {j, 0, n-k}];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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