A293966 Number of sets of exactly four 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.

4, 22, 116, 482, 1966, 7682, 29845, 115438, 449870, 1770788, 7073065, 28727652, 118907910, 502249944, 2167410896, 9563204836, 43166853057, 199391604156, 942578850020, 4559743209208, 22566589645408, 114215149597312, 590875202641724, 3122678708581528

Offset

8,1

Links

Alois P. Heinz, Table of n, a(n) for n = 8..805

Formula

a(n) = [x^n y^4] 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, 5)
    end:
a:= n-> coeff(b(n$2), x, 4):
seq(a(n), n=8..33);

Crossrefs

Column k=4 of A293815.

Cf. A000085.

Sequence in context: A290591 A272435 A106835 * A305554 A291183 A374454

Adjacent sequences: A293963 A293964 A293965 * A293967 A293968 A293969

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2017

Status

approved