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

11,1

Links

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

Formula

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

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);

Crossrefs

Column k=5 of A293815.

Cf. A000085.

Sequence in context: A056289 A056284 A366622 * A246587 A340309 A229504

Adjacent sequences: A293964 A293965 A293966 * A293968 A293969 A293970

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2017

Status

approved