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