A293737 Number of multisets of nonempty words with a total of n letters over septenary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
1, 1, 3, 7, 20, 54, 164, 500, 1629, 5462, 19164, 69457, 261154, 1012164, 4045640, 16611121, 70001515, 301922104, 1331128134, 5986321599, 27426419974, 127801386949, 605016657100, 2906093083727, 14149469612919, 69762426194708, 348016146152252, 1755188873640756
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Programs
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Maple
g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1], ((4*n^3+78*n^2+424*n+495)*g(n-1) +(n-1)*(34*n^2+280*n+ 305)*g(n-2) -2*(n-1)*(n-2)*(38*n+145)*g(n-3) -105*(n-1) *(n-2)*(n-3)*g(n-4))/((n+6)*(n+10)*(n+12))) end: a:= proc(n) option remember; `if`(n=0, 1, add(add(g(d) *d, d=numtheory[divisors](j))*a(n-j), j=1..n)/n) end: seq(a(n), n=0..35);
Formula
G.f.: Product_{j>=1} 1/(1-x^j)^A007578(j).
a(n) ~ c * 7^n / n^(21/2), where c = 233774941.39802934196800791705821024006230754487492494942398064537776753785... - Vaclav Kotesovec, May 30 2019
Comments