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A320734 Number of partitions of n with three sorts of part 1 which are introduced in ascending order.

%I A320734 #8 Dec 07 2020 08:11:37
%S A320734 1,1,3,7,19,52,151,442,1314,3921,11737,35171,105464,316318,948863,
%T A320734 2846461,8539221,25617443,76852054,230555794,691666924,2075000173,
%U A320734 6224999772,18674998357,56024993883,168074980137,504224938548,1512674813304,4538024437036
%N A320734 Number of partitions of n with three sorts of part 1 which are introduced in ascending order.
%H A320734 Alois P. Heinz, <a href="/A320734/b320734.txt">Table of n, a(n) for n = 0..2097</a>
%p A320734 b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
%p A320734       Stirling2(n, j), j=0..3), add(b(n-i*j, i-1), j=0..n/i))
%p A320734     end:
%p A320734 a:= n-> b(n$2):
%p A320734 seq(a(n), n=0..40);
%t A320734 b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 3}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
%t A320734 a[n_] := b[n, n];
%t A320734 a /@ Range[0, 40] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A320734 Column k=3 of A292745.
%K A320734 nonn
%O A320734 0,3
%A A320734 _Alois P. Heinz_, Oct 20 2018