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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. 1
1, 1, 4, 17, 92, 572, 4156, 34159, 314368, 3199844, 35703996, 433421495, 5687955724, 80256874912, 1211781887796, 19496946534720, 333041104402860, 6019770246910128, 114794574818830716, 2303332661416242633 (list; graph; refs; listen; history; internal format)
OFFSET

1,3

FORMULA

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

EXAMPLE

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).

MAPLE

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

CROSSREFS

Cf. A003319, A000142.

Sequence in context: A058279 A143405 A141154 * A020011 A067084 A123750

Adjacent sequences:  A112351 A112352 A112353 * A112355 A112356 A112357

KEYWORD

nonn

AUTHOR

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

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Last modified February 16 01:56 EST 2012. Contains 205860 sequences.