OFFSET
0,3
COMMENTS
a(n) is the determinant of the symmetric matrix (if(j<=floor((i+j)/2), 2^j*J(j+1),
2^i*J(i+1)))_{0<=i,j<=n}, where J(n)=A001045(n).
FORMULA
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}}.
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
EXAMPLE
a(3)=280 since det[1, 1, 1, 1; 1, 2, 2, 2; 1, 2, 12, 12; 1, 2, 12, 40]=280.
MATHEMATICA
Table[Product[4^k/2+(-2)^k/2, {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 11 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Feb 16 2011
STATUS
approved