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A293964 Number of sets of exactly two 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
2, 5, 18, 52, 168, 533, 1792, 6161, 22088, 81690, 313224, 1239532, 5068320, 21355130, 92714368, 413915690, 1899260064, 8941932948, 43168351136, 213385326440, 1079240048256, 5578228370404, 29443746273792, 158547032884868, 870370433845888, 4866859874106392 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..801

FORMULA

a(n) = [x^n y^2] 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, 3)

    end:

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

seq(a(n), n=3..30);

CROSSREFS

Column k=2 of A293815.

Cf. A000085.

Sequence in context: A183365 A295905 A056296 * A275079 A148417 A148418

Adjacent sequences:  A293961 A293962 A293963 * A293965 A293966 A293967

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2017

STATUS

approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)