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A292844
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Number of sets of nonempty words with a total of n letters over 10-ary alphabet.
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3
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1, 10, 145, 2120, 29660, 406752, 5475160, 72591320, 950032770, 12294612660, 157545928646, 2001232474600, 25222164942650, 315640538122100, 3924720693484450, 48514280936275240, 596460638741281825, 7296675024124004450, 88849865885787401525, 1077249149081661058800
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Product_{j>=1} (1+x^j)^(10^j).
a(n) ~ 10^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(10^(m-1)-1)) = 0.05242033574521236673164923513877706425... - Vaclav Kotesovec, Sep 28 2017
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MAPLE
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h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1)*binomial(10^i, j), j=0..n/i)))
end:
a:= n-> h(n$2):
seq(a(n), n=0..30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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