1,3

Prod_{k>=1} 1/(1-q^k)^{a(k)} = Sum_{n>=0} n! x^n

a(3) = 4 because (123), (213), (132) and (1,21) are all Lyndon

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

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).

read transfoms; EULERi([seq(n!, n=1..30)]);

Cf. A003319, A000142.

Sequence in context: A135168 A058279 A141154 this_sequence A020011 A067084 A123750

Adjacent sequences: A112351 A112352 A112353 this_sequence A112355 A112356 A112357

nonn

Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Sep 05 2005