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 A187652 #17 May 25 2025 10:11:24
%S A187652 1,0,10,194,5932,237624,11820780,702992968,48662470640,3843811669088,
%T A187652 341207224961856,33627579102171680,3643463136559851440,
%U A187652 430456189350273371648,55075003474909952394848,7586546772496980353804704
%N A187652 Alternated binomial cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).
%F A187652 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*abs(Stirling1(2*k,k)).
%F A187652 a(n) ~ c * d^n * (n-1)!, where d = 8*w^2/(2*w-1), where w = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... and c = exp((1-2*w)/(8*w^2)) / (2^(3/2)*Pi*sqrt(w-1)) = exp(-1/d) / (2^(3/2)*Pi*sqrt(w-1)) = 0.11686978539934159049334861225275481804523808136863346883911376048... - _Vaclav Kotesovec_, Jul 05 2021, updated May 25 2025
%p A187652 seq(sum((-1)^(n-k)*binomial(n,k)*abs(combinat[stirling1](2*k,k)),k=0..n),n=0..12);
%t A187652 Table[Sum[(-1)^(n - k)Binomial[n, k]Abs[StirlingS1[2k, k]], {k, 0, n}], {n, 0, 15}]
%o A187652 (Maxima) makelist(sum((-1)^(n-k)*binomial(n,k)*abs(stirling1(2*k,k)),k,0,n),n,0,12);
%Y A187652 Cf. A187646.
%K A187652 nonn,easy
%O A187652 0,3
%A A187652 _Emanuele Munarini_, Mar 12 2011