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A320822 Number of partitions of n with exactly nine sorts of part 1 which are introduced in ascending order.

%I A320822 #4 Oct 21 2018 12:48:12
%S A320822 1,45,1156,22321,360704,5158652,67512671,826325926,9601854284,
%T A320822 107074391802,1155110296163,12128784832510,124544257464575,
%U A320822 1255354199998891,12457896065009874,122014591067156240,1181759128040203056,11337243349606910986,107879491494316487583
%N A320822 Number of partitions of n with exactly nine sorts of part 1 which are introduced in ascending order.
%H A320822 Alois P. Heinz, <a href="/A320822/b320822.txt">Table of n, a(n) for n = 9..1053</a>
%F A320822 a(n) = A320740(n) - A320739(n).
%p A320822 b:= proc(n, i, k) option remember; `if`(n=0 or i<2, add(
%p A320822       Stirling2(n, j), j=0..k), add(b(n-i*j, i-1, k), j=0..n/i))
%p A320822     end:
%p A320822 a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(9):
%p A320822 seq(a(n), n=9..35);
%Y A320822 Column k=9 of A292746.
%Y A320822 Cf. A320739, A320740.
%K A320822 nonn
%O A320822 9,2
%A A320822 _Alois P. Heinz_, Oct 21 2018