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A320821 Number of partitions of n with exactly eight sorts of part 1 which are introduced in ascending order.

%I A320821 #4 Oct 21 2018 12:44:08
%S A320821 1,36,751,11917,159815,1912316,21084803,218711887,2164920950,
%T A320821 20657703246,191440769945,1732792167043,15385193971985,
%U A320821 134455882817716,1159708265019855,9893526482067374,83627808435796896,701411197245083482,5844301347854288709,48423747013469923303
%N A320821 Number of partitions of n with exactly eight sorts of part 1 which are introduced in ascending order.
%H A320821 Alois P. Heinz, <a href="/A320821/b320821.txt">Table of n, a(n) for n = 8..1112</a>
%F A320821 a(n) = A320739(n) - A320738(n).
%p A320821 b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(
%p A320821       Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))
%p A320821     end:
%p A320821 a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(8):
%p A320821 seq(a(n), n=8..35);
%Y A320821 Column k=8 of A292746.
%Y A320821 Cf. A320738, A320739.
%K A320821 nonn
%O A320821 8,2
%A A320821 _Alois P. Heinz_, Oct 21 2018