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A253190
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Triangle T(n, m)=Sum_{k=1..(n-m)/2} C(m+k-1, k)*T((n-m)/2, k), T(n,n)=1.
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3
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1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 3, 0, 1, 0, 3, 0, 4, 0, 1, 2, 0, 6, 0, 5, 0, 1, 0, 6, 0, 10, 0, 6, 0, 1, 3, 0, 13, 0, 15, 0, 7, 0, 1, 0, 11, 0, 24, 0, 21, 0, 8, 0, 1, 5, 0, 27, 0, 40, 0, 28, 0, 9, 0, 1, 0, 20, 0, 55, 0, 62, 0, 36, 0, 10, 0, 1
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OFFSET
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1,8
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LINKS
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FORMULA
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G.f.: A(x)^m=Sum_{n>=m} T(n,m)x^n, A(x)=Sum_{n>0} a(n)*x^(2*n-1), a(n) - is A000621.
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EXAMPLE
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1;
0, 1;
1, 0, 1;
0, 2, 0, 1;
1, 0, 3, 0, 1;
0, 3, 0, 4, 0, 1;
2, 0, 6, 0, 5, 0, 1;
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MAPLE
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option remember;
if n = m then
1;
elif type(n-m, 'odd') then
0 ;
else
add(binomial(m+k-1, k)*procname((n-m)/2, k), k=1..(n-m)/2) ;
end if;
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PROG
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(Maxima)
T(n, m):=if n=m then 1 else sum(binomial(m+k-1, k)*T((n-m)/2, k), k, 1, (n-m)/2);
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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