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%I #12 Oct 18 2018 17:24:07
%S 1,9,90,819,7461,67239,606051,5455359,49106502,441967518,3977783082,
%T 35800130448,322201861893,2899817511237,26098363809063,
%U 234885281153616,2113967586352095,19025708339182545,171231375557145825,1541082380573345274,13869741429702220707
%N Number of partitions of n into 9 sorts of parts.
%H Alois P. Heinz, <a href="/A246941/b246941.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{i>=1} 1/(1-9*x^i).
%F a(n) ~ c * 9^n, where c = Product_{k>=1} 1/(1-1/9^k) = 1.1408227572644372820166... . - _Vaclav Kotesovec_, Mar 19 2015
%F G.f.: Sum_{i>=0} 9^i*x^i/Product_{j=1..i} (1 - x^j). - _Ilya Gutkovskiy_, Oct 18 2018
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p b(n, i-1) +`if`(i>n, 0, 9*b(n-i, i))))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..25);
%t (O[x]^20 - 8/QPochhammer[9, x])[[3]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)
%Y Column k=9 of A246935.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Sep 08 2014
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