A097147 Total sum of minimum block sizes in all partitions of n-set.

1, 3, 7, 21, 66, 258, 1079, 4987, 25195, 136723, 789438, 4863268, 31693715, 217331845, 1564583770, 11795630861, 92833623206, 760811482322, 6479991883525, 57256139503047, 523919025038279, 4956976879724565, 48424420955966635, 487810283307069696

Offset: 1

Author

Vladeta Jovovic, Jul 27 2004

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..576

Crossrefs

Cf. A028417, A028418, A046746, A006128, A097145, A097146, A097148.

Column k=1 of A319298.

Programs

Maple

g:= proc(n, i, p) option remember; `if`(n=0, (i+1)*p!,
      `if`(i<1, 0, add(g(n-i*j, i-1, p+j*i)/j!/i!^j, j=0..n/i)))
    end:
a:= n-> g(n$2, 0):
seq(a(n), n=1..30);  # Alois P. Heinz, Mar 06 2015

Mathematica

Drop[Apply[Plus,Table[nn=25;Range[0,nn]!CoefficientList[Series[Exp[Sum[ x^i/i!,{i,n,nn}]]-1,{x,0,nn}],x],{n,1,nn}]],1]  (* Geoffrey Critzer, Jan 10 2013 *)
g[n_, i_, p_] := g[n, i, p] = If[n == 0, (i+1)*p!, If[i<1, 0,
     Sum[g[n-i*j, i-1, p+j*i]/j!/i!^j, {j, 0, n/i}]]];
a[n_] := g[n, n, 0];
Array[a, 30] (* Jean-François Alcover, Aug 24 2021, after Alois P. Heinz *)

Formula

E.g.f.: Sum_{k>0} (-1+exp(Sum_{j>=k} x^j/j!)).

Extensions

More terms from Max Alekseyev, Apr 29 2010