%I #17 Oct 08 2017 20:26:56
%S 1,2,18,262,4498,88174,1989162,51366438,1491069602,47749828830,
%T 1664928894170,62693869629142,2534737217687378,109469680507411214,
%U 5025930552213949450,244236790780300327302,12515419830686362586882
%N E.g.f. exp(Sum_{d|M} (exp(d*x)-1)/d), M=13.
%C Also the number of partitions of {1..(13n)} that are invariant under a permutation consisting of n 13-cycles. - _Danny Rorabaugh_, Oct 29 2015
%H Vincenzo Librandi, <a href="/A141009/b141009.txt">Table of n, a(n) for n = 0..200</a>
%H T. S. Motzkin, <a href="/A000262/a000262.pdf">Sorting numbers for cylinders and other classification numbers</a>, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
%H OEIS Wiki, <a href="http://oeis.org/wiki/Sorting_numbers">Sorting numbers</a>
%t u[0, j_]: = 1; u[k_, j_]: = u[k, j] = Sum[Binomial[k-1, i-1]Plus@@(u[k-i, j]#^(i-1)&/@Divisors[j]), {i, k}]; Table[u[n, 13], {n, 0, 30}] (* _Vincenzo Librandi_, Dec 12 2012, after _Wouter Meeussen_ in similar sequences *)
%t mx = 16; p = 13; Range[0, mx]! CoefficientList[ Series[ Exp[ (Exp[p*x] - p - 1)/p + Exp[x]], {x, 0, mx}], x] (* _Robert G. Wilson v_, Dec 12 2012 *)
%Y Column 13 of A162663.
%K nonn
%O 0,2
%A _R. J. Mathar_, Jul 11 2008