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 A352905 #10 Jul 15 2024 08:33:54
%S A352905 0,1,2,5,16,56,218,937,4376,22027,118744,681570,4144988,26598313,
%T A352905 179451366,1268930969,9378332608,72267300476,579336907254,
%U A352905 4822070246225,41597773001612,371306237988959,3424303740576440,32583334570211654,319487530199710232,3224337031346853361
%N A352905 Expansion of e.g.f. sin(x) * exp(exp(x) - 1).
%C A352905 The first negative term is a(71).
%F A352905 a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n,2*k+1) * Bell(n-2*k-1).
%F A352905 Conjecture: a(n) = (i/(2*e))*Sum_{k=0..oo} ((k - i)^n - (k + i)^n)/(k!), where i = sqrt(-1) and e = exp(1). - _Velin Yanev_, Jul 06 2024
%t A352905 nmax = 25; CoefficientList[Series[Sin[x] Exp[Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t A352905 Table[Sum[(-1)^k Binomial[n, 2 k + 1] BellB[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}], {n, 0, 25}]
%Y A352905 Cf. A000110, A009542, A102286, A351745.
%K A352905 sign
%O A352905 0,3
%A A352905 _Ilya Gutkovskiy_, Apr 07 2022