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.
terms = 20;
permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t k; s += t]; s!/m];
b[k_, q_] := If[OddQ[q], If[OddQ[k], 0, j = k/2; q^j (2 j)!/(j! 2^j)], Sum[ Binomial[k, 2 j] q^j (2 j)!/(j! 2^j), {j, 0, Quotient[k, 2]}]];
pm[v_] := Module[{p = Total[x^v]}, Product[ b[Coefficient[p, x, i], i], {i, 1, Exponent[p, x]}]];
a2830[n_] := Module[{s = 0}, Do[ s += permcount[p] pm[p]^3, {p, IntegerPartitions[2 n]}]; s/(2 n)!];
G[x_] = 1 + Sum[a2830[n] x^n, {n, 1, terms+1}];
gf = Sum[MoebiusMu[k] Log[G[x^k]]/k, {k, 1, terms+1}] + O[x]^(terms+1);
CoefficientList[gf, x] // Rest (* Jean-François Alcover, Jul 02 2018, after Andrew Howroyd *)
dpermcount(v) = {my(m=1,s=0,k=0,t); for(i=1,#v,t=v[i]; k=if(i>1&&t==v[i-1],k+1,1); m*=2*t*k;s+=2*t); s!/m}
S(n,x)={vector(n, n, if(n>1, sum(k=0, n, binomial(2*n-k,k)*2*n/(2*n-k)*x^k), 0))}
q(n,s)={my(t=0); if(n>1, forpart(p=n, t+=dpermcount(p)*prod(i=1, #p, s[p[i]]), [2,n])); t}
a(n)={my(p=q(n,S(n,x))); sum(i=0, poldegree(p), polcoeff(p,n-i)*(-1)^(n-i)*(2*i)!/(2^i*i!))} \\ Andrew Howroyd, Dec 18 2017
permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t k; s += t]; s!/m];
b[k_, q_] := If[OddQ[q], If[OddQ[k], 0, j = k/2; q^j (2 j)!/(j! 2^j)], Sum[ Binomial[k, 2 j] q^j (2 j)!/(j! 2^j), {j, 0, Quotient[k, 2]}]];
pm[v_] := Module[{p = Total[x^v]}, Product[b[Coefficient[p, x, i], i], {i, 1, Exponent[p, x]}]];
a[n_] := Module[{s = 0}, Do[s += permcount[p] pm[p]^3, {p, IntegerPartitions[2 n]}]; s/(2 n)!];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 30}] (* Jean-François Alcover, Jul 02 2018, after Andrew Howroyd *)
b(k,r) = {if(k%2, if(r%2, 0, my(j=r/2); k^j*(2*j)!/(j!*2^j)), sum(j=0, r\2, binomial(r, 2*j)*k^j*(2*j)!/(j!*2^j)))}
g(n,k)={sum(r=0, n\k, x^(k*r)*b(k,r)^3/(r!*k^r)) + O(x*x^n)}
seq(n)={Vec(substpol(prod(k=1, 2*n, g(2*n,k)), x^2, x))} \\ Andrew Howroyd, Dec 14 2017; updated May 02 2023
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