A073225 a(n) = ceiling(n^n/n!).

1, 1, 2, 5, 11, 27, 65, 164, 417, 1068, 2756, 7148, 18614, 48639, 127464, 334865, 881658, 2325751, 6145597, 16263867, 43099805, 114356612, 303761261, 807692035, 2149632062, 5726042116, 15264691108, 40722913455, 108713644517

Offset: 0

Author

Michael Somos, Jul 22 2002

Keywords

• nonn

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

Examples

			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 + ...
		

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

Crossrefs

Cf. A055775, A094082.

Programs

Magma

[Ceiling(n^n/Factorial(n)): n in [0..50]]; // G. C. Greubel, May 29 2018

Mathematica

Join[{1}, Table[Ceiling[n^n/n!], {n,1,50}]] (* G. C. Greubel, May 29 2018 *)

PARI

{a(n) = ceil(n^n / n!)}