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 A217487 #11 Nov 27 2017 11:47:34
%S A217487 1,10,299,21908,2901717,602319006,180257075455,73470070612264,
%T A217487 39124516839956393,26373727254869321522,21951183825927218885331,
%U A217487 22108623093930072226980540,26501124576166085360405809789,37282620382364481062065321327558
%N A217487 Partial sums of the squares of the numbers in sequence A080253.
%F A217487 a(n) = sum(c(k)^2,k=0..n), where c(n) = A080253(n).
%F A217487 a(n) ~ (n!)^2 * 2^(2*n-1) / (log(2))^(2*n + 2). - _Vaclav Kotesovec_, Nov 27 2017
%t A217487 t[n_] := Sum[StirlingS2[n, k] k!, {k, 0, n}]; c[n_] := Sum[Binomial[n, k] 2^k t[k], {k, 0, n}]; Table[Sum[c[k]^2, {k,0,n}], {n,0,100}]
%o A217487 (Maxima) t(n):=sum(stirling2(n,k)*k!,k,0,n);
%o A217487 c(n):=sum(binomial(n,k)*2^k*t(k),k,0,n);
%o A217487 makelist(sum(c(k)^2,k,0,n),n,0,40);
%Y A217487 Cf. A080253, A000670, A217483, A217484, A217485, A217486, A217488.
%K A217487 nonn
%O A217487 0,2
%A A217487 _Emanuele Munarini_, Oct 04 2012