login
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.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 21 2017
STATUS
approved