Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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