A004204 Number of permutations of length n with spread 0. (Formerly M3569)

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

Offset

1,4

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)

Prog

(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

Crossrefs

Sequence in context: A187116 A340903 A098541 * A160567 A034216 A144009

Adjacent sequences: A004201 A004202 A004203 * A004205 A004206 A004207

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved