A294006 Number of multisets 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.

1, 2, 7, 22, 73, 234, 791, 2702, 9507, 34258, 126807, 482306, 1885031, 7578028, 31316391, 133117500, 581531653, 2611112712, 12037781812, 56962049532, 276345797775, 1373655295948, 6988160240848, 36356528106984, 193225799686632, 1048279646446240

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..803

Formula

a(n) = [x^n y^4] 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, 5)
    end:
a:= n-> coeff(b(n$2), x, 4):
seq(a(n), n=4..35);

Crossrefs

Column k=4 of A293808.

Cf. A000085.

Sequence in context: A162770 A116387 A337805 * A322573 A294007 A294008

Adjacent sequences: A294003 A294004 A294005 * A294007 A294008 A294009

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2017

Status

approved