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.

A024218 a(n) = s(1)*s(2)*...*s(n+1)(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c=(-1)^n+1 and s(k) = 3k-2 for k = 1,2,3,...

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%I A024218 #11 Jan 02 2020 04:17:09
%S A024218 1,3,58,474,11224,155016,4516912,88578480,3088805440,78711944640,
%T A024218 3204477861760,100604441589120,4688743517516800,175033337095142400,
%U A024218 9194586775173990400,397954301618843289600,23270065752049280819200,1145878628833500097536000
%N A024218 a(n) = s(1)*s(2)*...*s(n+1)(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c=(-1)^n+1 and s(k) = 3k-2 for k = 1,2,3,...
%H A024218 Andrew Howroyd, <a href="/A024218/b024218.txt">Table of n, a(n) for n = 1..100</a>
%F A024218 a(n) ~ sqrt(2*Pi) * (9 - sqrt(3)*Pi - 3*log(2)) * 3^(n - 1) * n^(n + 5/6) / (Gamma(1/3) * exp(n)). - _Vaclav Kotesovec_, Jan 02 2020
%t A024218 Table[Product[3*k - 2, {k, 1, n+1}] * Sum[(-1)^k/(3*k - 2), {k, 2, n+1}], {n, 1, 20}] (* _Vaclav Kotesovec_, Jan 02 2020 *)
%o A024218 (PARI) a(n)={my(s=vector(n+1, k, 3*k-2)); vecprod(s)*sum(k=2, #s, (-1)^k/s[k])} \\ _Andrew Howroyd_, Jan 01 2020
%Y A024218 Cf. A024397.
%K A024218 nonn
%O A024218 1,2
%A A024218 _Clark Kimberling_
%E A024218 Terms a(13) and beyond from _Andrew Howroyd_, Jan 01 2020