A180589 a(n) = floor(n!*h(n)/n), where h(n) = Sum_{k=1..n} 1/k.

1, 1, 3, 12, 54, 294, 1866, 13698, 114064, 1062864, 10958530, 123870240, 1523289156, 20247546240, 289277533440, 4420892649600, 71965034739952, 1243166003251200, 22713955095665178, 437647401838080000, 8868800513341440000, 188567126333429760000, 4197346376195350706086

Offset: 1

Author

Gary Detlefs, Sep 10 2010

Keywords

• nonn

Crossrefs

Cf. A000254, A061006.

Programs

Maple

h:= n->sum(1/k,k=1..n):seq(floor(n!*h(n)/n),n=1..25);

Mathematica

a[n_]:=Floor[n!*Sum[1/k,{k,n}]/n]; Array[a,23] (* Stefano Spezia, Apr 20 2025 *)

Formula

a(n) = (A000254(n) - A061006(n))/n.

Extensions

a(21)-a(23) from Stefano Spezia, Apr 20 2025