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A119366
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Number of rooted planar n-trees whose number of leaves is equal to 1 modulo 3.
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3
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0, 1, 1, 1, 2, 11, 51, 177, 519, 1513, 5042, 18866, 71270, 257974, 905425, 3193737, 11578842, 42930441, 159998493, 593445318, 2194106568, 8138471667, 30399156174, 114219616809, 430344635913, 1622777285682, 6125465491551
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OFFSET
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0,5
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COMMENTS
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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)=1, (1/n)*C(n,k)*C(n,k+1), 0)}
a(0)=0, a(n)=sum{k=0..floor(n/3), (1/n)*C(n,3k+1)C(n,3k)},n>0; - Paul Barry, Jan 25 2007
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MAPLE
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if n = 0 then
0;
else
add(binomial(n, 3*k+1)*binomial(n, 3*k), k=0..n/3) ;
%/n ;
end if;
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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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