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Number of parts in all partitions of n with largest multiplicity six.
2

%I #6 Oct 25 2018 05:32:50

%S 6,0,7,7,15,15,38,39,67,84,131,160,242,293,421,537,730,912,1234,1533,

%T 2021,2525,3269,4053,5185,6394,8080,9948,12425,15219,18893,23006,

%U 28319,34379,42024,50788,61736,74279,89795,107674,129483,154660,185221,220424,262820

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

%H Alois P. Heinz, <a href="/A320376/b320376.txt">Table of n, a(n) for n = 6..1000</a>

%F a(n) ~ log(7) * exp(2*Pi*sqrt(n/7)) / (2 * Pi * 7^(1/4) * 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])(6):

%p seq(a(n), n=6..50);

%Y Column k=6 of A213177.

%K nonn

%O 6,1

%A _Alois P. Heinz_, Oct 11 2018