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.
G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 49*x^6 +... where A(x) = 1/((1-x)*(1-x^2)*(1-2*x^3)*(1-4*x^4)*(1-9*x^5)*(1-20*x^6)*(1-49*x^7)...).
b:= proc(n, i) option remember; `if`(i>n, 0,
a(i-1)*`if`(i=n, 1, b(n-i, i)))+`if`(i>1, b(n, i-1), 0)
end:
a:= n-> `if`(n=0, 1, b(n, n)):
seq(a(n), n=0..40); # Alois P. Heinz, Jul 20 2012
b[n_, i_] := b[n, i] = If[i>n, 0, a[i-1]*If[i == n, 1, b[n-i, i]]] + If[i>1, b[n, i-1], 0]; a[n_] := If[n == 0, 1, b[n, n]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 15 2015, after Alois P. Heinz *)
{a(n) = polcoeff(prod(i=0,n-1,1/(1-a(i)*x^(i+1)))+x*O(x^n),n)}
for(n=0,25,print1(a(n),", "))
{a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,1/m*sum(k=1,n, polcoeff(A+O(x^k), k-1)^m*x^(m*k)) +x*O(x^n))));polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))
G.f.: A(x) = 1 + 3*x + 12*x^2 + 64*x^3 + 354*x^4 + 2160*x^5 + 13518*x^6 +... where A(x) = ((1+x)*(1+3*x^2)*(1+12*x^3)*(1+64*x^4)*(1+354*x^5)*...)^3. Related expansion: A(x)^(1/3) = 1 + x + 3*x^2 + 15*x^3 + 76*x^4 + 454*x^5 + 2742*x^6 +...
A:= proc(n) option remember; local i, p, q; if n=0 then 1 else
p, q:= A(n-1), 1; for i from 0 to n-1 do q:= convert(
series(q*(1+coeff(p, x, i)*x^(i+1))^3, x, n+1), polynom)
od: q fi
end:
a:= n-> coeff(A(n), x, n):
seq(a(n), n=0..30); # Alois P. Heinz, Aug 01 2013
a[n_] := a[n] = SeriesCoefficient[Product[(1+a[k] x^(k+1))^3, {k, 0, n-1}], {x, 0, n}];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 20 2020 *)
{a(n) = polcoeff(prod(k=0, n-1, (1+a(k)*x^(k+1)+x*O(x^n)))^3, n)}
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