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.

A158621 Partial products of A001093.

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%I A158621 #9 Oct 15 2017 11:58:44
%S A158621 9,252,16380,2063880,447861960,154064514240,79035095805120,
%T A158621 57695619937737600,57753315557675337600,76927416322823549683200,
%U A158621 133007502822161917402252800,292350491203111894450151654400
%N A158621 Partial products of A001093.
%C A158621 A158620(n) = PRODUCT[k=2..n](k^3-1). A158622(n) is the numerator of the reduced fraction A158620(n)/A158621(n). A158623(n) is the denominator of the reduced fraction A158620(n)/A158621(n).
%F A158621 PRODUCT[k=2..n](k^3+1) = PRODUCT[k=2..n]A001093(k).
%F A158621 a(n) ~ sqrt(2*Pi) * cosh(sqrt(3)*Pi/2) * n^(3*n+3/2) / exp(3*n). - _Vaclav Kotesovec_, Jul 11 2015
%e A158621 a(2) = 2^3+1 = 9. a(3) = (2^3+1)*(3^3+1) = 9 * 28 = 252. a(4) = (2^3+1)*(3^3+1)*(4^3+1) = 9 * 28 * 65 = 16380.
%t A158621 Table[Product[(k^3+1),{k,2,n}],{n,2,20}] (* _Vaclav Kotesovec_, Jul 11 2015 *)
%t A158621 FoldList[Times,Range[2,20]^3+1] (* _Harvey P. Dale_, Oct 15 2017 *)
%Y A158621 Cf. A001093, A016921, A068601, A158620, A158622-A158624, A255433.
%K A158621 easy,nonn
%O A158621 2,1
%A A158621 _Jonathan Vos Post_, Mar 23 2009