A292718 - OEIS

%I #10 Sep 22 2017 09:44:21

%S 1,1,4,14,43,139,495,1544,5111,17348,55520,181946,607300,1951262,

%T 6362769,20972812,67451405,218884282,715353298,2298626230,7429125757,

%U 24124615697,77400570114,249285637563,805472940377,2579640351769,8283108375403,26655874638762

%N Number of multisets of nonempty words with a total of n letters over ternary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%H Alois P. Heinz, <a href="/A292718/b292718.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{j>=1} 1/(1-x^j)^A092255(j).

%F Euler transform of A092255.

%p b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,

%p       add(b(n-j, j, t-1)/j!, j=i..n/t))

%p     end:

%p a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*

%p       b(d, 0, 3), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)

%p     end:

%p seq(a(n), n=0..35);

%Y Column k=3 of A292712.

%Y Cf. A092255, A226873.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 21 2017