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A320378 Number of parts in all partitions of n with largest multiplicity eight.

%I A320378 #6 Oct 25 2018 05:33:28
%S A320378 8,0,9,9,19,19,40,40,81,93,140,173,267,315,461,572,779,970,1314,1619,
%T A320378 2152,2662,3442,4265,5468,6706,8502,10434,13065,15969,19853,24130,
%U A320378 29769,36093,44166,53357,64957,78120,94585,113406,136564,163163,195657,232927,278157
%N A320378 Number of parts in all partitions of n with largest multiplicity eight.
%H A320378 Alois P. Heinz, <a href="/A320378/b320378.txt">Table of n, a(n) for n = 8..1000</a>
%F A320378 a(n) ~ log(3) * exp(4*Pi*sqrt(n/3)/3) / (Pi * sqrt(2) * 3^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 25 2018
%p A320378 b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A320378       add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
%p A320378     end:
%p A320378 a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(8):
%p A320378 seq(a(n), n=8..50);
%Y A320378 Column k=8 of A213177.
%K A320378 nonn
%O A320378 8,1
%A A320378 _Alois P. Heinz_, Oct 11 2018