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 A356011 #15 Aug 11 2025 06:22:07
%S A356011 1,2,6,17,80,337,2240,14681,117010,1023941,10900472,108881665,
%T A356011 1375544846,17732140805,247041590476,3605768497217,59990390084690,
%U A356011 977383707751621,18214603019184800,337615168055209601,6763842079452393622,141262515443311046885
%N A356011 a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)).
%F A356011 E.g.f.: -(1/(1-x)) * Sum_{k>0} (1 - x^k) * log(1 - x^k)/k!.
%F A356011 a(n) ~ exp(1) * (n-1)!. - _Vaclav Kotesovec_, Aug 11 2025
%t A356011 Table[n! * Sum[1/(k!*Floor[n/k]), {k,1,n}], {n,1,25}] (* _Vaclav Kotesovec_, Aug 11 2025 *)
%o A356011 (PARI) a(n) = n!*sum(k=1, n, 1/(k!*(n\k)));
%o A356011 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, (1-x^k)*log(1-x^k)/k!)/(1-x)))
%Y A356011 Row sums of A356013.
%Y A356011 Cf. A345682, A345683, A355991, A356015.
%K A356011 nonn
%O A356011 1,2
%A A356011 _Seiichi Manyama_, Jul 23 2022