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 A306335 #11 Feb 10 2019 17:08:39
%S A306335 1,1,1,-1,4,-21,133,-981,8244,-77694,811194,-9292075,115843000,
%T A306335 -1561272571,22618147199,-350481556959,5784147674772,-101284047800632,
%U A306335 1875504207906184,-36616289396963678,751702523788615816,-16187581390548113842,364861626149143519378,-8590429045711448354359
%N A306335 Expansion of e.g.f. BesselI(0,2*log(1 + x)) + BesselI(1,2*log(1 + x)).
%H A306335 Robert Israel, <a href="/A306335/b306335.txt">Table of n, a(n) for n = 0..400</a>
%F A306335 a(n) = Sum_{k=0..n} Stirling1(n,k)*A001405(k).
%p A306335 E:= BesselI(0,2*log(1 + x)) + BesselI(1,2*log(1 + x)):
%p A306335 S:= series(E,x,51):
%p A306335 seq(coeff(S,x,j)*j!,j=0..50); # _Robert Israel_, Feb 10 2019
%t A306335 nmax = 23; CoefficientList[Series[BesselI[0, 2 Log[1 + x]] + BesselI[1, 2 Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
%t A306335 Table[Sum[StirlingS1[n, k] Binomial[k, Floor[k/2]], {k, 0, n}], {n, 0, 23}]
%o A306335 (PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(k, k\2)); \\ _Michel Marcus_, Feb 09 2019
%Y A306335 Cf. A001405, A048994, A086672, A305560.
%K A306335 sign
%O A306335 0,5
%A A306335 _Ilya Gutkovskiy_, Feb 08 2019