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A294011 Number of multisets of exactly nine 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, 818, 2824, 10004, 36252, 134583, 512580, 2002550, 8036582, 33117812, 140269222, 610272640, 2728310488, 12523401416, 59010337316, 285150731417, 1412280452528, 7161224109072, 37149235934192, 196939443174176, 1066080526789082 (list; graph; refs; listen; history; text; internal format)
OFFSET
9,2
LINKS
FORMULA
a(n) = [x^n y^9] 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, 10)
end:
a:= n-> coeff(b(n$2), x, 9):
seq(a(n), n=9..40);
CROSSREFS
Column k=9 of A293808.
Cf. A000085.
Sequence in context: A294008 A294009 A294010 * A294012 A293809 A307976
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 21 2017
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)