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 A217488 #13 Jun 02 2025 08:09:14
%S A217488 1,8,281,21328,2858481,596558808,179058197641,73110755339168,
%T A217488 38977936014004961,26295624802015360168,21898514473870334203641,
%U A217488 22064773395630274673891568,26456951179676525013504937681,37229662306608638451691410580088
%N A217488 Alternating sums of the squares of the numbers in sequence A080253.
%F A217488 a(n) = sum((-1)^(n-k)*c(k)^2,k=0..n), where c(n) = A080253(n).
%F A217488 a(n) ~ (n!)^2 * 2^(2*n-1) / (log(2))^(2*n + 2). - _Vaclav Kotesovec_, Nov 27 2017
%t A217488 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[(-1)^(n-k)c[k]^2, {k,0,n}], {n,0,100}]
%o A217488 (Maxima) t(n):=sum(stirling2(n,k)*k!,k,0,n);
%o A217488 c(n):=sum(binomial(n,k)*2^k*t(k),k,0,n);
%o A217488 makelist(sum((-1)^(n-k)*c(k)^2,k,0,n),n,0,40);
%Y A217488 Cf. A080253, A000670, A217483, A217484, A217485, A217486, A217487.
%K A217488 nonn
%O A217488 0,2
%A A217488 _Emanuele Munarini_, Oct 04 2012