%I A112354
%S A112354 1,1,4,17,92,572,4156,34159,314368,3199844,35703996,433421495,
%T A112354 5687955724,80256874912,1211781887796,19496946534720,333041104402860,
%U A112354 6019770246910128,114794574818830716,2303332661416242633
%N A112354 Inverse Euler transform of n!. Also the number of sequences of permutations 
               with no global descents which are Lyndon (smallest in lexicographic 
               order of all cyclic shifts of the sequences) where the size of the 
               sequence = sum of sizes of the permutations.
%F A112354 Prod_{k>=1} 1/(1-q^k)^{a(k)} = Sum_{n>=0} n! x^n
%e A112354 a(3) = 4 because (123), (213), (132) and (1,21) are all Lyndon
%e A112354 a(4) = 17 because there are 13 permutations with no global descents of 
               size 4 and (1,123), (1,213), (1,132) are all Lyndon
%e A112354 a(5) = 92 = 71 permutations with no global descents+13 sequences of the 
               form (1,pi) where pi in S_4 with no global descents+(1,1,1,21),(1,
               21,21),(1,1,123),(1,1,213),(1,1,132),(21,123),(21,213),(21,132).
%p A112354 read transfoms; EULERi([seq(n!,n=1..30)]);
%Y A112354 Cf. A003319, A000142.
%Y A112354 Sequence in context: A058279 A143405 A141154 this_sequence A020011 A067084 
               A123750
%Y A112354 Adjacent sequences: A112351 A112352 A112353 this_sequence A112355 A112356 
               A112357
%K A112354 nonn
%O A112354 1,3
%A A112354 Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Sep 05 2005