A004204 Number of permutations of length n with spread 0.

1, 1, 0, 4, 20, 144, 630, 5696, 39366, 366400, 3634950, 39066624, 479163828, 6226534272, 87238701000, 1315130458112, 20922813624336, 355586138666496, 6402373841107998, 121479626301440000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The spread of a permutation p is the sum of i*p(i) over 0 <= i < n, reduced modulo n. - Rintaro Matsuo, Nov 26 2022

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Rintaro Matsuo, Table of n, a(n) for n = 1..40
• R. L. Graham, and D. H. Lehmer, On the Permanent of Schur's Matrix, Jour. Australian Math. Soc. 21 no. 4 (series A) (1976), 487-497.
• Rintaro Matsuo, Code used to calculate up to a(40)

Crossrefs

Column k=0 of A147679.

Programs

PARI

a(n) = my(v=[1..n], nb=0); forperm(v, p, if (sum(i=1, n-1, Mod(i,n)*p[i]) == 0, nb++)); nb; \\ Michel Marcus, Nov 30 2022

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 17 2007