cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A191510 Product of terms in n-th row of A132818.

This page as a plain text file.
%I A191510 #23 Apr 16 2016 11:35:10
%S A191510 1,9,648,360000,1518750000,48243443062500,11480517255997440000,
%T A191510 20400479323264014247526400,270090559531318533654528000000000,
%U A191510 26599911685677709861296622500000000000000,19464564507161243794359748945629699456000000000000
%N A191510 Product of terms in n-th row of A132818.
%C A191510 Lim_{n -> inf} (a(n)*a(n+2))/a(n+1)^2 = e^2.  Like A168510, this limit is asymptotic from above.
%H A191510 H. J. Brothers and J. A. Knox, <a href="http://www.brotherstechnology.com/docs/mi_paper1.pdf">New closed-form approximations to the logarithmic constant e</a>, Math. Intelligencer, Vol. 20, No. 4, (1998), 25-29.
%F A191510 a(n)=product[product[((k + 1)/(k - 1))^k, {k, 2, j}], {j, 1, n}].
%F A191510 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 Glaisher-Kinkelin constant. - _Vaclav Kotesovec_, Jul 11 2015
%e A191510 For n=3, row 3 of A132818 = {6,18,6} and a(3)=648.
%t A191510 Table[Product[Product[((k + 1)/(k - 1))^k, {k, 2, j}], {j, 1, n}], {n, 1, 11}]
%t A191510 Table[(n + 1)^n * Hyperfactorial[n]^2 / (2^n * BarnesG[n+2]^2), {n, 1, 12}] (* _Vaclav Kotesovec_, Jul 11 2015 *)
%Y A191510 Cf. A132818, A002457. Related to e as in the cases of A168510 and A001142.
%K A191510 easy,nonn,nice
%O A191510 1,2
%A A191510 _Harlan J. Brothers_, Jun 04 2011