OFFSET
0,3
COMMENTS
The van der Waerden conjecture, now a theorem thanks to Egorycev, states that the permanent of any n X n doubly stochastic matrix is >= n!/n^n, with equality iff the matrix has all entries equal to 1/n.
Therefore the reciprocal of the permanent of any n X n doubly stochastic matrix is bounded from above by n^n/n! and this sequence.
n^n/n! = A001142(n)/A001142(n-1), where A001142(n) is product{k=0 to n} C(n,k) (where C() is a binomial coefficient). - Leroy Quet, May 01 2004
REFERENCES
G. P. Egorycev, Solution of the van der Waerden problem for permanents (Russian), Preprint IFSO-13 M. Akad. Nauk SSSR Sibirsk. Otdel., Inst. Fiz., Krasnoyarsk, 1980. 12 pp. Math. Rev. 82e:15006.
J. H. van Lint, R. M. Wilson, A Course in Combinatorics, Cambridge Univ. Press, 1992. p. 86.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
EXAMPLE
G.f.: 1 + x + 2*x^2 + 5*x^3 + 11*x^4 + 27*x^5 + 65*x^6 + 164*x^7 + 417*x^8 + ...
MATHEMATICA
Join[{1}, Table[Ceiling[n^n/n!], {n, 1, 50}]] (* G. C. Greubel, May 29 2018 *)
PROG
(PARI) {a(n) = ceil(n^n / n!)}
(Magma) [Ceiling(n^n/Factorial(n)): n in [0..50]]; // G. C. Greubel, May 29 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jul 22 2002
STATUS
approved