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A320379 Number of parts in all partitions of n with largest multiplicity nine.

%I A320379 #6 Oct 25 2018 05:33:48
%S A320379 9,0,10,10,21,21,44,44,80,101,152,178,279,330,476,594,813,1004,1359,
%T A320379 1669,2208,2743,3540,4365,5610,6876,8697,10669,13349,16290,20258,
%U A320379 24603,30334,36773,44999,54312,66122,79490,96214,115337,138887,165891,198941,236783
%N A320379 Number of parts in all partitions of n with largest multiplicity nine.
%H A320379 Alois P. Heinz, <a href="/A320379/b320379.txt">Table of n, a(n) for n = 9..1000</a>
%F A320379 a(n) ~ log(10) * exp(Pi*sqrt(3*n/5)) / (2 * Pi * 15^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 25 2018
%p A320379 b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A320379       add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
%p A320379     end:
%p A320379 a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(9):
%p A320379 seq(a(n), n=9..50);
%Y A320379 Column k=9 of A213177.
%K A320379 nonn
%O A320379 9,1
%A A320379 _Alois P. Heinz_, Oct 11 2018