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.
%I A352638 #23 Jun 25 2025 06:27:13
%S A352638 1,3,18,159,1872,27543,486288,10016619,235798272,6244714443,
%T A352638 183756215808,5947907121879,210026879004672,8034293365747743,
%U A352638 330982609573398528,14609181655918083939,687820834029346947072,34407546247054875367443,1822450167175258689896448
%N A352638 Expansion of e.g.f. 1/(1 - 3*sin(x)).
%F A352638 a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n,2*k+1) * a(n-2*k-1).
%F A352638 a(n) ~ n! / (2^(3/2) * arcsin(1/3)^(n+1)). - _Vaclav Kotesovec_, Mar 26 2022
%F A352638 a(n) = Sum_{k=0..n} 3^k * k! * i^(n-k) * A136630(n,k), where i is the imaginary unit. - _Seiichi Manyama_, Jun 25 2025
%t A352638 With[{m = 17}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*Sin[x]), {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o A352638 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*sin(x))))
%o A352638 (PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*binomial(n, 2*k+1)*a(n-2*k-1)));
%Y A352638 Cf. A000111, A007289.
%Y A352638 Cf. A107403, A352640.
%Y A352638 Cf. A136630.
%K A352638 nonn
%O A352638 0,2
%A A352638 _Seiichi Manyama_, Mar 25 2022