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A320739 Number of partitions of n with eight sorts of part 1 which are introduced in ascending order.

%I A320739 #8 Dec 07 2020 09:04:14
%S A320739 1,1,3,7,20,63,233,966,4454,22403,121570,705150,4337883,28091897,
%T A320739 190105229,1334705996,9656244012,71551215515,540187472767,
%U A320739 4137336876098,32036946594336,250131019258467,1965050543015106,15509209887539395,122829846706462146
%N A320739 Number of partitions of n with eight sorts of part 1 which are introduced in ascending order.
%H A320739 Alois P. Heinz, <a href="/A320739/b320739.txt">Table of n, a(n) for n = 0..1112</a>
%p A320739 b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
%p A320739       Stirling2(n, j), j=0..8), add(b(n-i*j, i-1), j=0..n/i))
%p A320739     end:
%p A320739 a:= n-> b(n$2):
%p A320739 seq(a(n), n=0..40);
%t A320739 b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 8}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
%t A320739 a[n_] := b[n, n];
%t A320739 a /@ Range[0, 40] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A320739 Column k=8 of A292745.
%K A320739 nonn
%O A320739 0,3
%A A320739 _Alois P. Heinz_, Oct 20 2018