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 A290716 #37 Feb 16 2025 08:33:50
%S A290716 1,1,1,3,15,35,225,1197,6881,45369,327375,2460755,19925367,171368067,
%T A290716 1551364997,14763620445,147405166785,1538113071857,16732908859599,
%U A290716 189413984297187,2226589748578775,27130592749003275,342118450334269917,4458168165784234253,59952936723606219009
%N A290716 Number of minimal dominating sets in the n-triangular (Johnson) graph.
%C A290716 A minimal dominating set on the triangular graph corresponds either with a minimal edge cover on the complete graph minus one vertex or with a perfect matching on the complete graph. Perfect matchings on the complete graph exists only for even n. - _Andrew Howroyd_, Aug 13 2017
%C A290716 Also the number of maximal irredundant sets in the n-triangular graph. - _Eric W. Weisstein_, Dec 31 2017
%H A290716 Vincenzo Librandi, <a href="/A290716/b290716.txt">Table of n, a(n) for n = 0..100</a>
%H A290716 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JohnsonGraph.html">Johnson Graph</a>
%H A290716 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIrredundantSet.html">Maximal Irredundant Set</a>
%H A290716 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>
%H A290716 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGraph.html">Triangular Graph</a>
%F A290716 a(n) = n*A053530(n-1) for n odd, a(n) = (n-1)!! + n*A053530(n-1) for n even. - _Andrew Howroyd_, Aug 13 2017
%F A290716 E.g.f.: exp(x^2/2) + x*exp(x*exp(x) - (x+x^2/2)). - _Andrew Howroyd_, Apr 21 2018
%t A290716 b[n_]:=n! Sum[1/k! (Binomial[k, n - k] 2^(k - n) (-1)^k + Sum[Binomial[k, j] Sum[j^(i - j)/(i - j)! Binomial[k - j, n - i - k + j] 2^(i - j + k - n) (-1)^(k - j), {i, j, n - k + j}], {j, k}]), {k, n}]; Join[{1, 1}, Table[n b[n - 1] + If[Mod[n, 2] == 0, (n - 1)!!, 0], {n, 2, 20}]] (* _Eric W. Weisstein_, Aug 14 2017 *)
%t A290716 Range[0, 20]! CoefficientList[Series[Exp[x^2/2] + x Exp[x Exp[x] - (x + x^2/2)], {x, 0, 20}], x] (* _Eric W. Weisstein_, Apr 23 2018 *)
%o A290716 (PARI) \\ here b(n) is A053530, df(n) is (2*n-1)!! = A001147
%o A290716 b(n)=polcoeff(serlaplace(exp(-x-1/2*x^2+x*exp(x+O(x^(n+1))))),n,x);
%o A290716 df(n)=polcoeff(serlaplace((1-2*x+O(x^(n+1)))^(-1/2)),n,x);
%o A290716 a(n) = n*b(n-1) + if(n%2==0, df(n/2), 0); \\ _Andrew Howroyd_, Aug 13 2017
%o A290716 (PARI) seq(n)={Vec(serlaplace(exp(x^2/2 + O(x*x^n)) + x*exp(x*exp(x + O(x^n)) - (x+x^2/2))))} \\ _Andrew Howroyd_, Apr 21 2018
%Y A290716 Cf. A001147, A053530, A290847.
%K A290716 nonn
%O A290716 0,4
%A A290716 _Eric W. Weisstein_, Aug 09 2017
%E A290716 a(8)-a(24) from formula by _Andrew Howroyd_, Aug 13 2017
%E A290716 a(0)-a(1) prepended by _Andrew Howroyd_, Apr 21 2018