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 A217483 #11 Nov 27 2017 06:20:41
%S A217483 1,2,15,132,1565,22918,400939,8160008,189453369,4942271754,
%T A217483 143128015943,4556517918604,158167223290453,5945611873120910,
%U A217483 240619359452963427,10430922482219093520,482234053313600047217,23683786738296923795986
%N A217483 Alternating sums of the numbers in sequence A080253.
%F A217483 a(n) = sum((-1)^(n-k)*c(k),k=0..n), where c(n) = A080253(n).
%F A217483 E.g.f.: exp(x)/(2-exp(2*x)) - (1/2)*exp(-x)*log(1/(2-exp(2*x))). - corrected by _Vaclav Kotesovec_, Nov 27 2017
%F A217483 a(n) ~ n! * 2^(n - 1/2) / (log(2))^(n+1). - _Vaclav Kotesovec_, Nov 27 2017
%t A217483 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],{k,0,n}], {n, 0, 100}]
%t A217483 nmax = 20; CoefficientList[Series[E^x/(2 - E^(2*x)) + Log[2 - E^(2*x)] / (2*E^x), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Nov 27 2017 *)
%o A217483 (Maxima) t(n):=sum(stirling2(n,k)*k!,k,0,n);
%o A217483 c(n):=sum(binomial(n,k)*2^k*t(k),k,0,n);
%o A217483 makelist(sum((-1)^(n-k)*c(k),k,0,n),n,0,10);
%Y A217483 Cf. A080253, A000670, A217484, A217485, A217486, A217487, A217488.
%K A217483 nonn
%O A217483 0,2
%A A217483 _Emanuele Munarini_, Oct 04 2012