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A261742 Number of partitions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order.

%I A261742 #13 May 10 2021 06:24:36
%S A261742 1,8,100,920,8986,77000,690652,5752280,48916087,401709720,3324377084,
%T A261742 26996501992,220265771738,1777445952616,14377907329724,
%U A261742 115613187110872,930725344479074,7467529999843432,59954521406306500,480433200037686456,3851244156978563566
%N A261742 Number of partitions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order.
%H A261742 Alois P. Heinz, <a href="/A261742/b261742.txt">Table of n, a(n) for n = 0..1000</a>
%F A261742 a(n) ~ c * 8^n, where c = Product_{k>=2} 1/(1 - binomial(k+7,7)/8^k) = 3.3565128773700137140303140039343582841894554205106317247... - _Vaclav Kotesovec_, Oct 11 2017, updated May 10 2021
%F A261742 G.f.: Product_{k>=1} 1 / (1 - binomial(k+7,7)*x^k). - _Ilya Gutkovskiy_, May 10 2021
%p A261742 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A261742       b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+7, 7))))
%p A261742     end:
%p A261742 a:= n-> b(n$2):
%p A261742 seq(a(n), n=0..30);
%Y A261742 Column k=8 of A261718.
%K A261742 nonn
%O A261742 0,2
%A A261742 _Alois P. Heinz_, Aug 30 2015