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A320377 Number of parts in all partitions of n with largest multiplicity seven.

%I A320377 #6 Oct 25 2018 05:33:08
%S A320377 7,0,8,8,17,17,36,43,74,85,136,167,254,308,437,550,754,944,1270,1581,
%T A320377 2088,2588,3356,4160,5326,6568,8306,10217,12776,15634,19413,23644,
%U A320377 29134,35360,43250,52285,63599,76547,92608,111079,133705,159774,191477,228012,272104
%N A320377 Number of parts in all partitions of n with largest multiplicity seven.
%H A320377 Alois P. Heinz, <a href="/A320377/b320377.txt">Table of n, a(n) for n = 7..1000</a>
%F A320377 a(n) ~ 3^(5/4) * log(2) * exp(Pi*sqrt(7*n/3)/2) / (2^(3/2) * 7^(1/4) * Pi * n^(1/4)). - _Vaclav Kotesovec_, Oct 25 2018
%p A320377 b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A320377       add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
%p A320377     end:
%p A320377 a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(7):
%p A320377 seq(a(n), n=7..50);
%Y A320377 Column k=7 of A213177.
%K A320377 nonn
%O A320377 7,1
%A A320377 _Alois P. Heinz_, Oct 11 2018