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A320375 Number of parts in all partitions of n with largest multiplicity five.

%I A320375 #9 Dec 13 2020 09:31:42
%S A320375 5,0,6,6,13,18,34,35,66,82,120,154,230,286,408,514,699,886,1189,1485,
%T A320375 1949,2441,3136,3906,4980,6159,7757,9555,11908,14600,18062,22000,
%U A320375 27028,32804,39996,48327,58614,70489,85036,101876,122284,145943,174419,207354,246804
%N A320375 Number of parts in all partitions of n with largest multiplicity five.
%H A320375 Alois P. Heinz, <a href="/A320375/b320375.txt">Table of n, a(n) for n = 5..1000</a>
%F A320375 a(n) ~ log(6) * exp(Pi*sqrt(5*n)/3) / (2 * Pi * 5^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 25 2018
%p A320375 b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A320375       add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
%p A320375     end:
%p A320375 a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(5):
%p A320375 seq(a(n), n=5..50);
%t A320375 b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[i < 1, {0, 0},        Sum[Function[l, {0, l[[1]] j} + l][b[n - i j, i - 1, k]], {j, 0, Min[n/i, k]}]]];
%t A320375 a[n_] := With[{k = 5}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
%t A320375 a /@ Range[5, 50] (* _Jean-François Alcover_, Dec 13 2020, after _Alois P. Heinz_ *)
%Y A320375 Column k=5 of A213177.
%K A320375 nonn
%O A320375 5,1
%A A320375 _Alois P. Heinz_, Oct 11 2018