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.

A140701 Partial products of A005448.

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%I A140701 #33 Feb 16 2025 08:33:08
%S A140701 1,1,4,40,760,23560,1083760,69360640,5895654400,642626329600,
%T A140701 87397180825600,14507932017049600,2887078471392870400,
%U A140701 678463440777324544000,185898982772986925056000,58744078556263868317696000,21206612358811256462688256000
%N A140701 Partial products of A005448.
%H A140701 Harvey P. Dale, <a href="/A140701/b140701.txt">Table of n, a(n) for n = 0..244</a> [a(0) added by Robert C. Lyons].
%H A140701 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%F A140701 a(n) = Product_{k=1..n} A005448(k).
%F A140701 a(n) ~ cosh(Pi*sqrt(5/3)/2) * 3^n * n^(2*n) / (exp(2*n) * 2^(n-1)). - _Vaclav Kotesovec_, Jul 11 2015
%F A140701 a(n) = (2/3)^(1 - n) * Pochhammer(1 + (3 - i*sqrt(15))/6, n - 1) * Pochhammer(1 + (3 + i*sqrt(15))/6, n - 1), for n>=1. - _Antonio GraciĆ” Llorente_, Sep 10 2023
%e A140701 a(10) = 87397180825600 = 1 * 4 * 10 * 19 * 31 * 46 * 64 * 85 * 109 * 136.
%t A140701 Table[Product[(3*k^2-3*k+2)/2,{k,1,n}],{n,1,20}] (* _Vaclav Kotesovec_, Jul 11 2015 *)
%t A140701 FoldList[Times,3*Accumulate[Range[0,20]]+1] (* _Harvey P. Dale_, Aug 05 2018 *)
%o A140701 (PARI) a(n) = prod(k=1, n, 3*k*(k-1)/2 + 1); \\ _Michel Marcus_, Mar 02 2023
%Y A140701 Cf. A005448.
%Y A140701 For analog with centered n-gonal numbers see A140702.
%Y A140701 For analog with regular triangular numbers see A006472.
%Y A140701 For the analog with a partial sum instead of a partial product see A006003.
%K A140701 nonn,easy
%O A140701 0,3
%A A140701 _Jonathan Vos Post_, May 24 2008