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A299026
Number of compositions of n whose standard factorization into Lyndon words has all weakly increasing factors.
4
1, 2, 4, 8, 16, 31, 59, 111, 205, 378, 685, 1238, 2213, 3940, 6955, 12221, 21333, 37074, 64073, 110267, 188877, 322244, 547522, 926903, 1563370, 2628008, 4402927, 7353656, 12244434, 20329271, 33657560, 55574996, 91525882, 150356718, 246403694, 402861907
OFFSET
1,2
LINKS
FORMULA
Euler transform of A167934.
EXAMPLE
The 2^6 - a(7) = 5 compositions of 7 whose Lyndon prime factors are not all weakly increasing: (11212), (1132), (1213), (1321), (142).
MATHEMATICA
nn=50;
ser=Product[1/(1-x^n)^(PartitionsP[n]-DivisorSigma[0, n]+1), {n, nn}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, nn}]
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={EulerT(vector(n, n, numbpart(n) - numdiv(n) + 1))} \\ Andrew Howroyd, Dec 01 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 01 2018
STATUS
approved