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.

A323715 a(n) = Product_{k=0..n} (2^k + 3^k).

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%I A323715 #14 Feb 08 2024 03:34:43
%S A323715 2,10,130,4550,441350,121371250,96247401250,222812733893750,
%T A323715 1518914406953693750,30674476448429845281250,
%U A323715 1842707823686526095580531250,330204028465507043697553297343750,176836474792332245660656600199579843750
%N A323715 a(n) = Product_{k=0..n} (2^k + 3^k).
%H A323715 G. C. Greubel, <a href="/A323715/b323715.txt">Table of n, a(n) for n = 0..64</a>
%F A323715 a(n) ~ c * 3^(n*(n+1)/2), where c = QPochhammer[-1, 2/3] = 10.934481779448897533...
%t A323715 Table[Product[2^k+3^k, {k, 0, n}], {n, 0, 12}]
%t A323715 Table[2^(n*(n+1)/2)*QPochhammer[-1, 3/2, n+1], {n, 0, 12}]
%o A323715 (PARI) a(n) = prod(k=0, n, 2^k+3^k); \\ _Michel Marcus_, Jan 25 2019
%o A323715 (Magma) [(&*[3^j+2^j: j in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Aug 30 2023
%o A323715 (SageMath) [product(3^j+2^j for j in range(n+1)) for n in range(21)] # _G. C. Greubel_, Aug 30 2023
%Y A323715 Cf. A000079, A000244, A007689, A323716, A369680.
%K A323715 nonn
%O A323715 0,1
%A A323715 _Vaclav Kotesovec_, Jan 25 2019