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A061778
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a(n) = Product_{j=0..floor(n/2)} binomial(n,j).
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1
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1, 2, 3, 24, 50, 1800, 5145, 878080, 3429216, 2857680000, 15219319500, 63117561830400, 457937132487120, 9577928124440387712, 94609025993497640625, 10077943267571584204800000
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listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..97
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FORMULA
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For odd n, a(n) = sqrt(A001142(n)); for even n, (a(n)^2)/A001405(n) = A001142(n).
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EXAMPLE
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n=5: a(5) = 1*5*10 = 50;
n=6: a(6) = 1*6*15*20 = 1800. [corrected by Jon E. Schoenfield, Jul 01 2018]
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MATHEMATICA
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Table[Apply[Times, Table[Binomial[n, j], {j, 0, Floor[n/2]}]], {w, 1, 20}]
Table[Product[Binomial[n, j], {j, 0, Floor[n/2]}], {n, 20}] (* Harvey P. Dale, Dec 06 2018 *)
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PROG
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(PARI) { for (n=1, 97, write("b061778.txt", n, " ", prod(j=0, n\2, binomial(n, j))) ) } \\ Harry J. Smith, Jul 27 2009
(GAP) List([1..20], n->Product([0..Int(n/2)], j->Binomial(n, j))); # Muniru A Asiru, Jul 01 2018
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CROSSREFS
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Cf. A001142, A001405.
Sequence in context: A257789 A336616 A354278 * A160667 A118204 A061355
Adjacent sequences: A061775 A061776 A061777 * A061779 A061780 A061781
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KEYWORD
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easy,nonn
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AUTHOR
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Labos Elemer, Jun 22 2001
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STATUS
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approved
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