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%I #10 Nov 13 2023 10:33:15
%S 1,0,11,214,6555,262770,13076765,777866388,53853263165,4254252038764,
%T 377667803463431,37222867283396314,4033161189724173207,
%U 476511397553009371918,60969023704806106263737,8398605422371512041566888
%N Alternated cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).
%F a(n) = sum((-1)^(n-k)s(2k,k)),k=0..n)
%F 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 seq(sum((-1)^(n-k)*abs(combinat[stirling1](2*k,k)),k=0..n),n=0..12);
%t Table[Sum[(-1)^(n-k)Abs[StirlingS1[2k, k]], {k, 0, n}], {n, 0, 15}]
%o (Maxima) makelist(sum((-1)^(n-k)*abs(stirling1(2*k,k)),k,0,n),n,0,12);
%Y Cf. A187646, A332928.
%K nonn,easy
%O 0,3
%A _Emanuele Munarini_, Mar 12 2011
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