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 A187650 #14 Oct 19 2024 08:33:12
%S A187650 1,0,11,214,6555,262770,13076765,777866388,53853263165,4254252038764,
%T A187650 377667803463431,37222867283396314,4033161189724173207,
%U A187650 476511397553009371918,60969023704806106263737,8398605422371512041566888
%N A187650 Alternated cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).
%F A187650 a(n) = Sum_{k=0..n} (-1)^(n-k)*s(2*k,k).
%F A187650 a(n) ~ 2^(3*n-1) * c^(2*n) * n^(n - 1/2) / (sqrt(Pi*(c-1)) * (2*c-1)^n * exp(n)), where c = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... - _Vaclav Kotesovec_, Jul 05 2021
%p A187650 seq(sum((-1)^(n-k)*abs(combinat[stirling1](2*k,k)),k=0..n),n=0..12);
%t A187650 Table[Sum[(-1)^(n-k)Abs[StirlingS1[2k, k]], {k, 0, n}], {n, 0, 15}]
%o A187650 (Maxima) makelist(sum((-1)^(n-k)*abs(stirling1(2*k,k)),k,0,n),n,0,12);
%Y A187650 Cf. A187646, A332928.
%K A187650 nonn,easy
%O A187650 0,3
%A A187650 _Emanuele Munarini_, Mar 12 2011