A097145 Total sum of minimum list sizes in all sets of lists of n-set, cf. A000262.

0, 1, 5, 25, 157, 1101, 9211, 85513, 900033, 10402633, 133059331, 1836961941, 27619253113, 444584808253, 7678546353843, 140944884572521, 2751833492404321, 56691826303303953, 1233793951629951043, 28191548364561422173, 676190806704598883241

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..444

Formula

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

Example

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.

Maple

b:= proc(n, m) option remember; `if`(n=0, m, add(j!*
      b(n-j, min(m, j))*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> `if`(n=0, 0, b(n, infinity)):
seq(a(n), n=0..25);  # Alois P. Heinz, May 10 2016

Mathematica

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 *)

Crossrefs

Cf. A000262, A028417, A028418, A046746, A006128, A097146-A097148.

Sequence in context: A090014 A249475 A179324 * A085644 A356599 A137963

Adjacent sequences: A097142 A097143 A097144 * A097146 A097147 A097148

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 27 2004

Extensions

More terms from Max Alekseyev, Jul 04 2009

a(0)=0 prepended by Alois P. Heinz, May 10 2016

Status

approved