A293967 Number of sets of exactly five nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

6, 48, 274, 1338, 6035, 25874, 108002, 444458, 1818905, 7451418, 30693022, 127604480, 536876960, 2291507552, 9939572897, 43885543586, 197465168488, 906430558822, 4247727231198, 20333276583188, 99450038211268, 497066503157976, 2538584563166367

Offset: 11

Author

Alois P. Heinz, Oct 20 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 11..807

Crossrefs

Column k=5 of A293815.

Cf. A000085.

Programs

Maple

g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 6)
    end:
a:= n-> coeff(b(n$2), x, 5):
seq(a(n), n=11..35);

Formula

a(n) = [x^n y^5] Product_{j>=1} (1+y*x^j)^A000085(j).