A185149 a(n) = 3^n*A003046(n+1)/A002457(n).

1, 1, 3, 27, 756, 68040, 20207880, 20228087880, 69422797604160, 828491666608045440, 34788365080871828025600, 5191328567558179408948185600, 2776779354844059467693477099212800, 5363460395055494624228658756213491712000

Offset

0,3

Comments

a(n) is the determinant of the symmetric matrix (if(j<=floor((i+j)/2), A000108(j+1), A000108(i+1)))_{0<=i,j<=n}.

Links

G. C. Greubel, Table of n, a(n) for n = 0..60

Formula

a(n) = Product_{k=0..(n-1)} (A000108(k+2) - A000108(k+1)).

a(n) = Product_{k=0..(n-1)} 3(k+1)*A000108(k+1)/(k+3).

a(n) = Product_{k=0..(n-1)} A000245(k+1).

a(n) = (A^(3/2) 2^(n(n+1))*2^(23/24)*3^n*Pi^(-1/4-n/2)*G(n+3/2)*Gamma(n+1)) /(e^(1/8)*G(n+4)), where G is Barnes G-function, and A is the Glaisher-Kinkelin constant (A074962) (reported by Wolfram Alpha).

a(n) ~ A^(3/2) * 2^(n^2+n+5/24) * 3^n * exp(3*n/2-1/8) / (n^(3*n/2+31/8) * Pi^(n/2+1)), where A = 1.2824271291... is the Glaisher-Kinkelin constant (see A074962). - Vaclav Kotesovec, Nov 14 2014

Mathematica

Table[Product[3*(2*k+2)!/((k+3)!*k!), {k, 0, n-1}], {n, 0, 10}] (* Vaclav Kotesovec, Nov 14 2014 *)

Crossrefs

Cf. A000108, A000245, A074962.

Cf. A087014, A087016, A087017 (some values of the Barnes G-function).

Sequence in context: A193610 A052269 A138525 * A326086 A194500 A012505

Adjacent sequences: A185146 A185147 A185148 * A185150 A185151 A185152

Keyword

nonn,easy

Author

Paul Barry, Feb 15 2011

Status

approved