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 A352150 #7 Mar 09 2022 10:40:56
%S A352150 0,1,-3,2,-6,-1,-5,132,1624,17145,174509,1789842,18659146,196678143,
%T A352150 2057524963,20460314396,171030108768,529697015489,-27050118799923,
%U A352150 -1079945984126798,-30289996673371254,-765129844741436785,-18575997643525737477,-444653043972658034044
%N A352150 a(n) = Sum_{k=0..n-1} (-1)^k * binomial(n,k)^2 * (n-k-1)!.
%F A352150 Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselJ(0,2*sqrt(x)) * (Ei(x) - log(x) - gamma).
%t A352150 Table[Sum[(-1)^k Binomial[n, k]^2 (n - k - 1)!, {k, 0, n - 1}], {n, 0, 23}]
%t A352150 nmax = 23; Assuming[x > 0, CoefficientList[Series[BesselJ[0, 2 Sqrt[x]] (ExpIntegralEi[x] - Log[x] - EulerGamma), {x, 0, nmax}], x]] Range[0, nmax]!^2
%o A352150 (PARI) a(n) = sum(k=0, n-1, (-1)^k * binomial(n,k)^2 * (n-k-1)!); \\ _Michel Marcus_, Mar 06 2022
%Y A352150 Cf. A002741, A009940, A352149.
%K A352150 sign
%O A352150 0,3
%A A352150 _Ilya Gutkovskiy_, Mar 06 2022