|
%I #12 Feb 18 2017 12:14:30
%S 0,1,5,25,157,1101,9211,85513,900033,10402633,133059331,1836961941,
%T 27619253113,444584808253,7678546353843,140944884572521,
%U 2751833492404321,56691826303303953,1233793951629951043,28191548364561422173,676190806704598883241
%N Total sum of minimum list sizes in all sets of lists of n-set, cf. A000262.
%H Alois P. Heinz, <a href="/A097145/b097145.txt">Table of n, a(n) for n = 0..444</a>
%F E.g.f.: Sum_{k>0} (exp(x^k/(1-x))-1).
%e For n=4 we have 73 sets of lists (cf. A000262): (1234) (24 ways), (123)(4) (6*4 ways), (12)(34) (3*4 ways), (12)(3)(4) (6*2 ways), (1)(2)(3)(4) (1 way); so a(n)= 24*4+24*1+12*2+12*1+1*1 = 157.
%p b:= proc(n, m) option remember; `if`(n=0, m, add(j!*
%p b(n-j, min(m, j))*binomial(n-1, j-1), j=1..n))
%p end:
%p a:= n-> `if`(n=0, 0, b(n, infinity)):
%p seq(a(n), n=0..25); # _Alois P. Heinz_, May 10 2016
%t b[n_, m_] := b[n, m] = If[n==0, m, Sum[j!*b[n-j, Min[m, j]]*Binomial[n-1, j - 1], {j, 1, n}]]; a[n_] := If[n==0, 0, b[n, Infinity]]; Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Feb 18 2017, after _Alois P. Heinz_ *)
%Y Cf. A000262, A028417, A028418, A046746, A006128, A097146-A097148.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Jul 27 2004
%E More terms from _Max Alekseyev_, Jul 04 2009
%E a(0)=0 prepended by _Alois P. Heinz_, May 10 2016
|
