A292718 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.

1, 1, 4, 14, 43, 139, 495, 1544, 5111, 17348, 55520, 181946, 607300, 1951262, 6362769, 20972812, 67451405, 218884282, 715353298, 2298626230, 7429125757, 24124615697, 77400570114, 249285637563, 805472940377, 2579640351769, 8283108375403, 26655874638762

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

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

Euler transform of A092255.

Maple

b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
      add(b(n-j, j, t-1)/j!, j=i..n/t))
    end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*
      b(d, 0, 3), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..35);

Crossrefs

Column k=3 of A292712.

Cf. A092255, A226873.

Sequence in context: A247470 A049539 A037528 * A212688 A261451 A084613

Adjacent sequences: A292715 A292716 A292717 * A292719 A292720 A292721

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2017

Status

approved