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a(n)=Product{k=0..n, A003665(k)}.
0

%I #9 Mar 18 2024 05:53:27

%S 1,1,10,280,38080,18887680,39286374400,319319651123200,

%T 10504339243348787200,1374135642457914946355200,

%U 721146385161913763847208960000,1511615130036671973985522422906880000,12683442560532981918553467630898150113280000,425533759542581882449393472981756918078982062080000

%N a(n)=Product{k=0..n, A003665(k)}.

%C a(n) is the determinant of the symmetric matrix (if(j<=floor((i+j)/2), 2^j*J(j+1),

%C 2^i*J(i+1)))_{0<=i,j<=n}, where J(n)=A001045(n).

%F a(n)=Product{k=0..n, 4^k/2+(-2)^k/2}=Product{k=0..n, sum{j=0..floor(k/2), binomial(n,2k)*9^k}}.

%F a(n) ~ c * 2^(n^2 - 1), where c = 2*QPochhammer(1/2, -1/2) = 1.1373978925308570119099534741488893085817049027787180586386880920367... . - _Vaclav Kotesovec_, Jul 11 2015, updated Mar 18 2024

%e a(3)=280 since det[1, 1, 1, 1; 1, 2, 2, 2; 1, 2, 12, 12; 1, 2, 12, 40]=280.

%t Table[Product[4^k/2+(-2)^k/2,{k,0,n}],{n,0,15}] (* _Vaclav Kotesovec_, Jul 11 2015 *)

%Y Cf. A186269.

%K nonn,easy

%O 0,3

%A _Paul Barry_, Feb 16 2011