

A191510


Product of terms in nth row of A132818.


0



1, 9, 648, 360000, 1518750000, 48243443062500, 11480517255997440000, 20400479323264014247526400, 270090559531318533654528000000000, 26599911685677709861296622500000000000000, 19464564507161243794359748945629699456000000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Lim_{n > inf} (a(n)*a(n+2))/a(n+1)^2 = e^2. Like A168510, this limit is asymptotic from above.


LINKS

Table of n, a(n) for n=1..11.
H. J. Brothers and J. A. Knox, New closedform approximations to the logarithmic constant e, Math. Intelligencer, Vol. 20, No. 4, (1998), 2529.


FORMULA

a(n)=product[product[((k + 1)/(k  1))^k, {k, 2, j}], {j, 1, n}].
a(n) ~ A^4 * exp(n^2 + 2*n + 5/6) / (n^(2/3) * 2^(2*n+1) * Pi^(n+1)), where A = A074962 = 1.2824271291... is the GlaisherKinkelin constant.  Vaclav Kotesovec, Jul 11 2015


EXAMPLE

For n=3, row 3 of A132818 = {6,18,6} and a(3)=648.


MATHEMATICA

Table[Product[Product[((k + 1)/(k  1))^k, {k, 2, j}], {j, 1, n}], {n, 1, 11}]
Table[(n + 1)^n * Hyperfactorial[n]^2 / (2^n * BarnesG[n+2]^2), {n, 1, 12}] (* Vaclav Kotesovec, Jul 11 2015 *)


CROSSREFS

Cf. A132818, A002457. Related to e as in the cases of A168510 and A001142.
Sequence in context: A210053 A128795 A323425 * A081232 A020548 A091062
Adjacent sequences: A191507 A191508 A191509 * A191511 A191512 A191513


KEYWORD

easy,nonn,nice


AUTHOR

Harlan J. Brothers, Jun 04 2011


STATUS

approved



