A320377 - OEIS

%I #6 Oct 25 2018 05:33:08

%S 7,0,8,8,17,17,36,43,74,85,136,167,254,308,437,550,754,944,1270,1581,

%T 2088,2588,3356,4160,5326,6568,8306,10217,12776,15634,19413,23644,

%U 29134,35360,43250,52285,63599,76547,92608,111079,133705,159774,191477,228012,272104

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

%H Alois P. Heinz, <a href="/A320377/b320377.txt">Table of n, a(n) for n = 7..1000</a>

%F 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 b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,

%p       add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))

%p     end:

%p a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(7):

%p seq(a(n), n=7..50);

%Y Column k=7 of A213177.

%K nonn

%O 7,1

%A _Alois P. Heinz_, Oct 11 2018