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A320819 Number of partitions of n with exactly six sorts of part 1 which are introduced in ascending order.

%I A320819 #5 Oct 21 2018 12:29:13
%S A320819 1,21,267,2668,23116,182443,1349703,9529538,64991613,431754668,
%T A320819 2810794455,18011999644,113994583260,714334592349,4440885185275,
%U A320819 27431944561645,168574045898166,1031553703902986,6290661582662655,38253841380267660,232085126723073278
%N A320819 Number of partitions of n with exactly six sorts of part 1 which are introduced in ascending order.
%H A320819 Alois P. Heinz, <a href="/A320819/b320819.txt">Table of n, a(n) for n = 6..1288</a>
%F A320819 a(n) = A320737(n) - A320736(n).
%p A320819 b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(
%p A320819       Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))
%p A320819     end:
%p A320819 a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(6):
%p A320819 seq(a(n), n=6..35);
%Y A320819 Column k=6 of A292746.
%Y A320819 Cf. A320736, A320737.
%K A320819 nonn
%O A320819 6,2
%A A320819 _Alois P. Heinz_, Oct 21 2018