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15, 126, 143, 1020, 399, 1150, 783, 8184, 1295, 3198, 1935, 9212, 2703, 6270, 3599, 65520, 4623, 10366, 5775, 25596, 7055, 15486, 8463, 73720, 9999, 21630, 11663, 50172, 13455, 28798, 15375, 524256, 17423, 36990
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OFFSET
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1,1
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COMMENTS
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This sequence is, via A220371, related to A220002, which is related to the Catalan numbers.
Information about the peculiar structure of the a(n) can be found in A220466.
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LINKS
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FORMULA
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a(2^p*(2*n-1)) = 2^p*(2^(2*p+4)*(2*n-1)^2-1), p >= 0.
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MAPLE
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nmax:= 34: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a(2^p*(2*n-1)) := 2^p*(2^(2*p+4)*(2*n-1)^2-1) od: od: seq(a(n), n=1..nmax);
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MATHEMATICA
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b[n_] := b[n] = 2^(2n) Product[2i+1, {i, 1, 2n}] GCD[n!, 2^n];
a[n_] := b[n]/(4 b[n-1]);
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PROG
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(Sage)
a = {}; z = 1; s = 0; p = 1
while s < len:
i = s; z += z
while i < len:
a[i] = p*((4*i+4)^2-1)
i += z
s += s + 1; p += p
return [a[i] for i in range(len)]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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