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 A260701 #25 Oct 21 2021 08:57:02
%S A260701 -1,2,-1,5,20,197,2219,30620,496565,9265037,195535514,4605925535,
%T A260701 119796721835,3410051954402,105449267146859,3520120318516625,
%U A260701 126168879827914580,4832661370036811417,197001989531658791879,8515772839409988885140,389080859811496699020425
%N A260701 a(n) = (-3*(-1)^n + Sum_{k>=0} A000108(k)*k^n/6^k)/sqrt(3), where A000108 are Catalan numbers.
%H A260701 Vaclav Kotesovec, <a href="/A260701/b260701.txt">Table of n, a(n) for n = 0..100</a>
%F A260701 Sum_{k >= 0} A000108(k)*k^n/6^k = a(n)*sqrt(3) + 3*(-1)^n.
%F A260701 a(n) ~ sqrt(2) * n^(n-1) / (sqrt(3) * exp(n) * log(3/2)^(n-1/2)). - _Vaclav Kotesovec_, Nov 17 2015
%F A260701 E.g.f.: -sqrt( exp(-x) * (-2+3*exp(-x)) ). - _Seiichi Manyama_, Oct 21 2021
%e A260701 For n = 5, Sum_{k>=0} A000108(k)*k^5/6^k = 197*sqrt(3) - 3, so a(5) = 197.
%t A260701 Table[(-3 (-1)^n + Sum[CatalanNumber[k] k^n/6^k, {k, 0, Infinity}])/Sqrt[3], {n, 0, 20}]
%o A260701 (PARI) vector(20, n, n--; round((suminf(k=0, binomial(2*k,k)/(k+1)*k^n/6^k) - 3*(-1)^n)/sqrt(3))) \\ _Altug Alkan_, Nov 16 2015
%o A260701 (PARI) N=20; x='x+O('x^N); Vec(serlaplace(-sqrt(exp(-x)*(-2+3*exp(-x))))) \\ _Seiichi Manyama_, Oct 21 2021
%Y A260701 Cf. A000108, A260902, A348468.
%K A260701 sign
%O A260701 0,2
%A A260701 _Vladimir Reshetnikov_, Nov 16 2015