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 A299027 Number of compositions of n whose standard factorization into Lyndon words has all distinct weakly increasing factors. 4
 1, 1, 3, 5, 11, 20, 38, 69, 125, 225, 400, 708, 1244, 2176, 3779, 6532, 11229, 19223, 32745, 55555, 93875, 158025, 265038, 443009, 738026, 1225649, 2029305, 3350167, 5515384, 9055678, 14830076, 24226115, 39480306, 64190026, 104130753, 168556588, 272268482 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 FORMULA Weigh transform of A167934. EXAMPLE The a(5) = 11 compositions:       (5) = (5)      (41) = (4)*(1)      (14) = (14)      (32) = (3)*(2)      (23) = (23)     (131) = (13)*(1)     (113) = (113)     (212) = (2)*(12)     (122) = (122)    (1121) = (112)*(1)    (1112) = (1112) Not included:     (311) = (3)*(1)*(1)     (221) = (2)*(2)*(1)    (2111) = (2)*(1)*(1)*(1)    (1211) = (12)*(1)*(1)   (11111) = (1)*(1)*(1)*(1)*(1) MATHEMATICA nn=50; ser=Product[(1+x^n)^(PartitionsP[n]-DivisorSigma[0, n]+1), {n, nn}]; Table[SeriesCoefficient[ser, {x, 0, n}], {n, nn}] PROG (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)} seq(n)={WeighT(vector(n, n, numbpart(n) - numdiv(n) + 1))} \\ Andrew Howroyd, Dec 01 2018 CROSSREFS Cf. A001045, A032153, A034691, A049311, A059966, A098407, A116540, A185700, A270995, A283877,  A292432, A293993, A296373, A299023, A299024, A299026. Sequence in context: A058932 A118037 A094588 * A339006 A247353 A293948 Adjacent sequences:  A299024 A299025 A299026 * A299028 A299029 A299030 KEYWORD nonn AUTHOR Gus Wiseman, Feb 01 2018 STATUS approved

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Last modified August 1 18:37 EDT 2021. Contains 346402 sequences. (Running on oeis4.)