A186270 a(n)=Product{k=0..n, A003665(k)}.

1, 1, 10, 280, 38080, 18887680, 39286374400, 319319651123200, 10504339243348787200, 1374135642457914946355200, 721146385161913763847208960000, 1511615130036671973985522422906880000, 12683442560532981918553467630898150113280000, 425533759542581882449393472981756918078982062080000

Offset: 0

Author

Paul Barry, Feb 16 2011

Keywords

• nonn
• easy

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).

Examples

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

Crossrefs

Cf. A186269.

Programs

Mathematica

Table[Product[4^k/2+(-2)^k/2,{k,0,n}],{n,0,15}] (* Vaclav Kotesovec, Jul 11 2015 *)

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