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 A317310 #33 Mar 27 2019 03:45:51
%S A317310 1,2,4,6,4,0,-2,14,-100,792,-6996,68508,-737882,8676200,-110627142,
%T A317310 1520662410,-22418697948,352885526856,-5907074659016,104782694989616,
%U A317310 -1963418893492364,38753471698684512,-803656781974363412,17469671114170029708,-397223288562294817330,9429329994809282773300
%N A317310 Expansion of e.g.f. (1 + x)^2*BesselI(0,2*log(1 + x)).
%F A317310 a(n) = Sum_{k=0..n} Stirling1(n,k)*A000984(k).
%p A317310 a:=series((1 + x)^2*BesselI(0,2*log(1 + x)), x=0, 26): seq(n!*coeff(a, x, n), n=0..25); # _Paolo P. Lava_, Mar 26 2019
%t A317310 nmax = 25; CoefficientList[Series[(1 + x)^2 BesselI[0, 2 Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
%t A317310 Table[Sum[StirlingS1[n, k] Binomial[2 k, k], {k, 0, n}], {n, 0, 25}]
%o A317310 (PARI) my(x='x + O('x^30)); Vec(serlaplace((1 + x)^2*besseli(0,2*log(1 + x)))) \\ _Michel Marcus_, Mar 27 2019
%Y A317310 Cf. A000984, A048994, A086672, A305406.
%K A317310 sign
%O A317310 0,2
%A A317310 _Ilya Gutkovskiy_, Jan 22 2019