%I #20 Aug 24 2021 07:01:30

%S 1,3,7,21,66,258,1079,4987,25195,136723,789438,4863268,31693715,

%T 217331845,1564583770,11795630861,92833623206,760811482322,

%U 6479991883525,57256139503047,523919025038279,4956976879724565,48424420955966635,487810283307069696

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

%H Alois P. Heinz, <a href="/A097147/b097147.txt">Table of n, a(n) for n = 1..576</a>

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

%p g:= proc(n, i, p) option remember; `if`(n=0, (i+1)*p!,

%p `if`(i<1, 0, add(g(n-i*j, i-1, p+j*i)/j!/i!^j, j=0..n/i)))

%p end:

%p a:= n-> g(n$2, 0):

%p seq(a(n), n=1..30); # _Alois P. Heinz_, Mar 06 2015

%t 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 *)

%t g[n_, i_, p_] := g[n, i, p] = If[n == 0, (i+1)*p!, If[i<1, 0,

%t Sum[g[n-i*j, i-1, p+j*i]/j!/i!^j, {j, 0, n/i}]]];

%t a[n_] := g[n, n, 0];

%t Array[a, 30] (* _Jean-François Alcover_, Aug 24 2021, after _Alois P. Heinz_ *)

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

%Y Column k=1 of A319298.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Jul 27 2004

%E More terms from _Max Alekseyev_, Apr 29 2010