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 A187651 #23 Oct 19 2024 08:33:16
%S A187651 1,0,6,71,1380,34854,1092317,40900215,1781924888,88569337730,
%T A187651 4946558473226,306691008191732,20903038895529727,1553426761730508586,
%U A187651 125016067017985968931,10831572432055401760624,1005245087722396707881648
%N A187651 Alternated binomial partial sums of the central Stirling numbers of the second kind.
%F A187651 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*S(2*k,k).
%F A187651 a(n) ~ c * d^n * (n-1)!, where d = 4/(w*(2-w)) = 6.176554609483480358231680164... and c = exp(w^2/4 - 1) / (Pi * sqrt(2*w * (1-w))) = 0.17569156962762991098958896633434384684339835018075095823375851..., where w = -LambertW(-2*exp(-2))^2 = -A226775. - _Vaclav Kotesovec_, Mar 30 2018, updated Jul 07 2021
%p A187651 seq(add((-1)^(n-k)*binomial(n,k)*combinat[stirling2](2*k,k), k=0..n), n=0..20);
%t A187651 Table[Sum[(-1)^(n-k)Binomial[n, k] StirlingS2[2k, k], {k, 0, n}], {n, 0, 16}]
%o A187651 (Maxima) makelist(sum((-1)^(n-k) *binomial(n,k) *stirling2(2*k,k), k,0,n), n,0,12);
%Y A187651 Cf. A187653.
%K A187651 nonn,easy
%O A187651 0,3
%A A187651 _Emanuele Munarini_, Mar 12 2011