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 A261743 Number of partitions of n where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order. 2

%I #11 May 10 2021 06:24:41

%S 1,9,126,1299,14211,136611,1373127,12838293,122478147,1129559068,

%T 10495764324,95773104459,877873080195,7963150929030,72400207009635,

%U 654588661768353,5924851016703093,53460853371243261,482688774419853026,4350478100196378069,39224153751141474936

%N Number of partitions of n where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order.

%H Alois P. Heinz, <a href="/A261743/b261743.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ c * 9^n, where c = Product_{k>=2} 1/(1 - binomial(k+8,8)/9^k) = 3.23950351986835655716873222462341048089067679826... - _Vaclav Kotesovec_, Oct 11 2017, updated May 10 2021

%F G.f.: Product_{k>=1} 1 / (1 - binomial(k+8,8)*x^k). - _Ilya Gutkovskiy_, May 10 2021

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+8, 8))))

%p end:

%p a:= n-> b(n\$2):

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

%Y Column k=9 of A261718.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Aug 30 2015

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Last modified August 10 21:39 EDT 2024. Contains 375058 sequences. (Running on oeis4.)