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A037293
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a(n) = Sum_{i=0..2^(n-1)} binomial(2^(n-1), i)^2.
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9
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1, 2, 6, 70, 12870, 601080390, 1832624140942590534, 23951146041928082866135587776380551750, 5768658823449206338089748357862286887740211701975162032608436567264518750790
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = A000984(2^(n-1)) = binomial(2^n,2^(n-1)) = (2^n)!/((2^(n-1))!)^2 for n > 0. - Martin Renner, Jan 16 2017
a(n) = (2^(2^n)*(2^n + 2)*(1/2*(2^n + 1))!)/(sqrt(Pi)*(2^n + 1)*(1/2*(2^n + 2))!) = (2^(2^n)*(2^n + 2)*Gamma((2^n+3)/2))/(sqrt(Pi)*(2^n + 1)*Gamma(2^(n-1)+2)) for n > 0. - Alexander R. Povolotsky, Nov 19 2022
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MAPLE
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a:= n-> (t-> binomial(t, iquo(t, 2)))(2^n):
#
a:=n->sum(binomial(2^(n-1), i)^2, i=0..2^(n-1)); seq(a(n), n=0..8);
a:=n->piecewise(n=0, 1, binomial(2^n, 2^(n-1))); seq(a(n), n=0..8); # Martin Renner, Jan 16 2017
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MATHEMATICA
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Flatten[{1, Table[Binomial[2^n, 2^(n-1)], {n, 1, 8}]}] (* Vaclav Kotesovec, Nov 13 2014 *)
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PROG
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(PARI) a(n) = sum(i=0, 2^(n-1), binomial(2^(n-1), i)^2) \\ Michel Marcus, Jun 09 2013
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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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EXTENSIONS
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STATUS
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approved
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