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 A191510 Product of terms in n-th 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 H. J. Brothers and J. A. Knox, New closed-form approximations to the logarithmic constant e, Math. Intelligencer, Vol. 20, No. 4, (1998), 25-29. 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 Glaisher-Kinkelin 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

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Last modified January 17 18:14 EST 2020. Contains 330987 sequences. (Running on oeis4.)