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A246940 Number of partitions of n into 8 sorts of parts.

%I A246940 #12 Apr 12 2018 22:23:42
%S A246940 1,8,72,584,4744,38024,304840,2439368,19520264,156167944,1249386824,
%T A246940 9995142472,79961491848,639692324232,5117541421512,40940334536648,
%U A246940 327522698972168,2620181617189384,20961453119350856,167691625158581832,1341533002724164744
%N A246940 Number of partitions of n into 8 sorts of parts.
%H A246940 Alois P. Heinz, <a href="/A246940/b246940.txt">Table of n, a(n) for n = 0..1000</a>
%F A246940 G.f.: Product_{i>=1} 1/(1-8*x^i).
%F A246940 a(n) ~ c * 8^n, where c = Product_{k>=1} 1/(1-1/8^k) = 1.1635943971944701027405... . - _Vaclav Kotesovec_, Mar 19 2015
%F A246940 G.f.: Sum_{i>=0} 8^i*x^i/Product_{j=1..i} (1 - x^j). - _Ilya Gutkovskiy_, Apr 12 2018
%p A246940 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A246940       b(n, i-1) +`if`(i>n, 0, 8*b(n-i, i))))
%p A246940     end:
%p A246940 a:= n-> b(n$2):
%p A246940 seq(a(n), n=0..25);
%t A246940 (O[x]^20 - 7/QPochhammer[8, x])[[3]] (* _Vladimir Reshetnikov_, Nov 20 2015 *)
%Y A246940 Column k=8 of A246935.
%K A246940 nonn
%O A246940 0,2
%A A246940 _Alois P. Heinz_, Sep 08 2014