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A320613 Number of parts in all partitions of n in which no part occurs more than ten times.

%I A320613 #10 Jul 31 2020 16:39:53
%S A320613 1,3,6,12,20,35,54,86,128,192,264,387,531,741,1001,1366,1809,2425,
%T A320613 3170,4172,5398,6997,8948,11482,14547,18451,23193,29157,36355,45347,
%U A320613 56150,69509,85565,105216,128732,157393,191545,232870,282033,341164,411251,495197,594369
%N A320613 Number of parts in all partitions of n in which no part occurs more than ten times.
%H A320613 Alois P. Heinz, <a href="/A320613/b320613.txt">Table of n, a(n) for n = 1..5000</a>
%F A320613 a(n) ~ 3^(1/4) * log(11) * exp(2*Pi*sqrt(5*n/33)) / (2 * Pi * 55^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 18 2018
%p A320613 b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(5*i*(i+1)<n, 0, add(
%p A320613       (l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 10))))
%p A320613     end:
%p A320613 a:= n-> b(n$2)[2]:
%p A320613 seq(a(n), n=1..50);
%t A320613 Table[Length[Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 10 &]]], {n, 43}] (* _Robert Price_, Jul 31 2020 *)
%Y A320613 Column k=10 of A210485.
%K A320613 nonn
%O A320613 1,2
%A A320613 _Alois P. Heinz_, Oct 17 2018