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A320820 Number of partitions of n with exactly seven sorts of part 1 which are introduced in ascending order.

%I A320820 #4 Oct 21 2018 12:34:29
%S A320820 1,28,463,5909,64479,633796,5786275,50033463,415225854,3338335646,
%T A320820 26179143977,201266007483,1522856635641,11374331041836,84061202478127,
%U A320820 615860361908534,4479596579257904,32388729758708314,233011769893620853,1669336230635613631
%N A320820 Number of partitions of n with exactly seven sorts of part 1 which are introduced in ascending order.
%H A320820 Alois P. Heinz, <a href="/A320820/b320820.txt">Table of n, a(n) for n = 7..1187</a>
%F A320820 a(n) = A320738(n) - A320737(n).
%p A320820 b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(
%p A320820       Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))
%p A320820     end:
%p A320820 a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(7):
%p A320820 seq(a(n), n=7..35);
%Y A320820 Column k=7 of A292746.
%Y A320820 Cf. A320737, A320738.
%K A320820 nonn
%O A320820 7,2
%A A320820 _Alois P. Heinz_, Oct 21 2018