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A292839 Number of sets of nonempty words with a total of n letters over 5-ary alphabet. 2
1, 5, 35, 260, 1805, 12376, 83175, 550775, 3600400, 23276175, 149012380, 945726575, 5955676150, 37243117575, 231412658225, 1429522303905, 8783382129825, 53700395135475, 326809026132350, 1980383108328950, 11952682268739660, 71870696616619250, 430632502970026125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: Product_{j>=1} (1+x^j)^(5^j).

a(n) ~ 5^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(5^(m-1)-1)) = 0.112852293193143374268678097722831649456... - 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(5^i, j), j=0..n/i)))

    end:

a:= n-> h(n$2):

seq(a(n), n=0..30);

CROSSREFS

Column k=5 of A292804.

Sequence in context: A193577 A196661 A104532 * A180900 A087630 A084135

Adjacent sequences:  A292836 A292837 A292838 * A292840 A292841 A292842

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 24 2017

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)