A294008 Number of multisets of exactly six 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, 818, 2816, 9967, 36080, 133875, 509676, 1990984, 7990628, 32936173, 139548808, 607402437, 2716780286, 12476624346, 58818236078, 284350933608, 1408898449946, 7146679566822, 37085526689402, 196654885016221, 1064783059174600

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..805

Formula

a(n) = [x^n y^6] 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, 7)
    end:
a:= n-> coeff(b(n$2), x, 6):
seq(a(n), n=6..35);

Crossrefs

Column k=6 of A293808.

Cf. A000085.

Sequence in context: A294006 A322573 A294007 * A294009 A294010 A294011

Adjacent sequences: A294005 A294006 A294007 * A294009 A294010 A294011

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2017

Status

approved