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%I #10 Dec 19 2020 03:23:11
%S 1,1,3,7,20,54,164,500,1630,5472,19257,70132,265845,1042187,4233556,
%T 17747898,76808746,342105748,1567582938,7371055703,35543320641,
%U 175391546006,884988267329,4558168670317,23945579145172,128119583103268,697657759802893,3861749505389798
%N Number of multisets of nonempty words with a total of n letters over denary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%C This sequence differs from A293110 first at n=11.
%C In general, for k>2, is column k of A293108 asymptotic to c(k) * k^n / n^(k*(k-1)/4), where c(k) are constants dependent only on k. - _Vaclav Kotesovec_, Dec 19 2020
%H Alois P. Heinz, <a href="/A293740/b293740.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{j>=1} 1/(1-x^j)^A212916(j).
%F a(n) ~ c * 10^n / n^(45/2), where c = 2738042932059662927432072.80048573... - _Vaclav Kotesovec_, Dec 19 2020
%Y Column k=10 of A293108.
%Y Cf. A212916, A293110, A293749.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Oct 15 2017
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