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%I #22 Sep 08 2022 08:45:06
%S 1,1,2,5,11,27,65,164,417,1068,2756,7148,18614,48639,127464,334865,
%T 881658,2325751,6145597,16263867,43099805,114356612,303761261,
%U 807692035,2149632062,5726042116,15264691108,40722913455,108713644517
%N a(n) = ceiling(n^n/n!).
%C 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.
%C 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.
%C 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
%D 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.
%D J. H. van Lint, R. M. Wilson, A Course in Combinatorics, Cambridge Univ. Press, 1992. p. 86.
%H G. C. Greubel, <a href="/A073225/b073225.txt">Table of n, a(n) for n = 0..1000</a>
%e 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 + ...
%t Join[{1}, Table[Ceiling[n^n/n!], {n,1,50}]] (* _G. C. Greubel_, May 29 2018 *)
%o (PARI) {a(n) = ceil(n^n / n!)}
%o (Magma) [Ceiling(n^n/Factorial(n)): n in [0..50]]; // _G. C. Greubel_, May 29 2018
%Y Cf. A055775, A094082.
%K nonn
%O 0,3
%A _Michael Somos_, Jul 22 2002
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