A294007 Number of multisets 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.

1, 2, 7, 22, 73, 240, 811, 2792, 9857, 35644, 132119, 502832, 1964131, 7885792, 32523695, 137915764, 600865387, 2690302074, 12367812720, 58364059306, 282421855885, 1400551909446, 7109841300492, 36919536804334, 195890584265442, 1061185175436116

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..804

Formula

a(n) = [x^n y^5] Product_{j>=1} 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 or i=1, x^n,
      add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 6)
    end:
a:= n-> coeff(b(n$2), x, 5):
seq(a(n), n=5..35);

Crossrefs

Column k=5 of A293808.

Cf. A000085.

Sequence in context: A337805 A294006 A322573 * A294008 A294009 A294010

Adjacent sequences: A294004 A294005 A294006 * A294008 A294009 A294010

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2017

Status

approved