|
%I #14 Jan 20 2022 07:44:31
%S 1,17,203119913336833
%N Number of social welfare functions according to the definition given by Kim and Roush for m=n, where m = number of persons and n = number of alternatives.
%H Thomas Wieder, Nov 06 2007, <a href="/A134686/b134686.txt">Table of n, a(n) for n = 1..4</a>
%H K. H. Kim and F. W. Roush, <a href="https://doi.org/10.1142/9789812799890_0003">Combinatorial Aspects of Mathematical Social Sciences</a>, in Sungpyo Hong, Jim Ho Kwah, Ki Hang and Fred W. Roush (eds.), Combinatorial and Computational Mathematics, World Scientific, 2001, ISBN 981-02-4678-1, pp. 30 - 55. See first formula on page 40.
%F a(n) = w(n, n) where w(m,n) = Sum_{k=1..m} (Stirling2(n,k)*k!)^(n!*m).
%p SWF:=proc() local m,mend,n,k,w; mend:=5; for m from 1 to mend do n:=m; w[m]:=sum((stirling2(n,k)*k!)^(n!*m), k=1..m); od; print(w[1],w[2],w[3],w[4],w[5],w[6],w[7],w[8],w[9],w[10]); end proc;
%o (PARI) w(m,n) = sum(k=1, m, (stirling(n,k,2)*k!)^(n!*m));
%o a(n) = w(n, n); \\ _Michel Marcus_, Jan 20 2022
%Y Cf. A000670, A082677, A082678.
%K nonn,bref
%O 1,2
%A _Thomas Wieder_, Nov 06 2007
|
