A356011 - OEIS

%I #12 Jul 23 2022 09:54:04

%S 1,2,6,17,80,337,2240,14681,117010,1023941,10900472,108881665,

%T 1375544846,17732140805,247041590476,3605768497217,59990390084690,

%U 977383707751621,18214603019184800,337615168055209601,6763842079452393622,141262515443311046885

%N a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)).

%F E.g.f.: -(1/(1-x)) * Sum_{k>0} (1 - x^k) * log(1 - x^k)/k!.

%o (PARI) a(n) = n!*sum(k=1, n, 1/(k!*(n\k)));

%o (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 Row sums of A356013.

%Y Cf. A345682, A345683, A355991, A356015.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jul 23 2022