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A292840 Number of sets of nonempty words with a total of n letters over 6-ary alphabet. 3
1, 6, 51, 452, 3777, 31074, 250735, 1993176, 15640983, 121378650, 932738805, 7105552308, 53709133137, 403124780178, 3006420386499, 22290321581448, 164378277308862, 1206180958964508, 8810022165617086, 64073173243207632, 464122836576398454, 3349321050668452460 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{j>=1} (1+x^j)^(6^j).
a(n) ~ 6^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(6^(m-1)-1)) = 0.091503304254691843343610606469481430508... - Vaclav Kotesovec, Sep 28 2017
MAPLE
h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1)*binomial(6^i, j), j=0..n/i)))
end:
a:= n-> h(n$2):
seq(a(n), n=0..30);
CROSSREFS
Column k=6 of A292804.
Sequence in context: A341424 A050916 A011790 * A356394 A202754 A363112
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 24 2017
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)