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%I #18 Feb 26 2022 14:35:09
%S 1,2,3,24,50,1800,5145,878080,3429216,2857680000,15219319500,
%T 63117561830400,457937132487120,9577928124440387712,
%U 94609025993497640625,10077943267571584204800000
%N a(n) = Product_{j=0..floor(n/2)} binomial(n,j).
%H Harry J. Smith, <a href="/A061778/b061778.txt">Table of n, a(n) for n = 1..97</a>
%F For odd n, a(n) = sqrt(A001142(n)); for even n, (a(n)^2)/A001405(n) = A001142(n).
%e n=5: a(5) = 1*5*10 = 50;
%e n=6: a(6) = 1*6*15*20 = 1800. [corrected by _Jon E. Schoenfield_, Jul 01 2018]
%t Table[Apply[Times, Table[Binomial[n, j], {j, 0, Floor[n/2]}]], {w, 1, 20}]
%t Table[Product[Binomial[n,j],{j,0,Floor[n/2]}],{n,20}] (* _Harvey P. Dale_, Dec 06 2018 *)
%o (PARI) { for (n=1, 97, write("b061778.txt", n, " ", prod(j=0, n\2, binomial(n, j))) ) } \\ _Harry J. Smith_, Jul 27 2009
%o (GAP) List([1..20],n->Product([0..Int(n/2)],j->Binomial(n,j))); # _Muniru A Asiru_, Jul 01 2018
%Y Cf. A001142, A001405.
%K easy,nonn
%O 1,2
%A _Labos Elemer_, Jun 22 2001