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, 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

Cf. A000670, A082677, A082678.

Sequence in context: A271562 A157255 A114432 * A257305 A128398 A257377

Adjacent sequences: A134683 A134684 A134685 * A134687 A134688 A134689

Keyword

nonn,bref

Author

Thomas Wieder, Nov 06 2007

Status

approved