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A293969 Number of sets of exactly seven 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, 40, 394, 2766, 16251, 86162, 426894, 2021990, 9290152, 41829426, 185965908, 820999576, 3615595261, 15941247432, 70583512572, 314664832674, 1415621796873, 6439720543682, 29674662921377, 138736843637738, 659019083032289, 3184439719295586, 15669157686000028 (list; graph; refs; listen; history; text; internal format)
OFFSET

17,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 17..813

FORMULA

a(n) = [x^n y^7] Product_{j>=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, 1, `if`(i<1, 0,

      add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 8)

    end:

a:= n-> coeff(b(n$2), x, 7):

seq(a(n), n=17..42);

CROSSREFS

Column k=7 of A293815.

Cf. A000085.

Sequence in context: A221820 A301528 A253132 * A168192 A251129 A007772

Adjacent sequences:  A293966 A293967 A293968 * A293970 A293971 A293972

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2017

STATUS

approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)