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.

A335630 Expansion of e.g.f. Product_{k>0} (1+tan(x)^k).

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%I A335630 #25 Oct 03 2020 04:05:40
%S A335630 1,1,2,14,64,616,5072,58064,669184,9417856,137019392,2294104064,
%T A335630 40350383104,778782954496,16050760435712,352024447115264,
%U A335630 8269739647565824,204097141026881536,5360540853755052032,147190808628196081664,4270498402940171321344,129024432217526266494976
%N A335630 Expansion of e.g.f. Product_{k>0} (1+tan(x)^k).
%H A335630 Vaclav Kotesovec, <a href="/A335630/b335630.txt">Table of n, a(n) for n = 0..200</a>
%F A335630 E.g.f.: exp( Sum_{k>0} (-tan(x))^k/(k*(tan(x)^k-1)) ).
%t A335630 nmax = 25; CoefficientList[Series[Product[1 + Tan[x]^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 03 2020 *)
%o A335630 (PARI) N=40; x='x+O('x^N); Vec(serlaplace(eta(tan(x)^2)/eta(tan(x))))
%o A335630 (PARI) N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1+tan(x)^k)))
%o A335630 (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, (-tan(x))^k/(k*(tan(x)^k-1))))))
%Y A335630 Cf. A000009, A000182, A335627, A335629.
%K A335630 nonn
%O A335630 0,3
%A A335630 _Seiichi Manyama_, Oct 02 2020