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A134686
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.
1
1, 17, 203119913336833
OFFSET
1,2
LINKS
Thomas Wieder, Nov 06 2007, Table of n, a(n) for n = 1..4
K. H. Kim and F. W. Roush, Combinatorial Aspects of Mathematical Social Sciences, 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.
FORMULA
a(n) = w(n, n) where w(m,n) = Sum_{k=1..m} (Stirling2(n,k)*k!)^(n!*m).
MAPLE
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;
PROG
(PARI) w(m, n) = sum(k=1, m, (stirling(n, k, 2)*k!)^(n!*m));
a(n) = w(n, n); \\ Michel Marcus, Jan 20 2022
CROSSREFS
KEYWORD
nonn,bref
AUTHOR
Thomas Wieder, Nov 06 2007
STATUS
approved