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A320735 Number of partitions of n with four sorts of part 1 which are introduced in ascending order.

%I A320735 #8 Dec 07 2020 08:24:09
%S A320735 1,1,3,7,20,62,217,803,3092,12128,48047,191266,763249,3049383,
%T A320735 12190360,48747140,194960047,779783252,3119019290,12475849884,
%U A320735 49902945245,199610872683,798441674561,3193763066392,12775045002551,51100165484967,204400632890492
%N A320735 Number of partitions of n with four sorts of part 1 which are introduced in ascending order.
%H A320735 Alois P. Heinz, <a href="/A320735/b320735.txt">Table of n, a(n) for n = 0..1663</a>
%p A320735 b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
%p A320735       Stirling2(n, j), j=0..4), add(b(n-i*j, i-1), j=0..n/i))
%p A320735     end:
%p A320735 a:= n-> b(n$2):
%p A320735 seq(a(n), n=0..40);
%t A320735 b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 4}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
%t A320735 a[n_] := b[n, n];
%t A320735 a /@ Range[0, 40] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A320735 Column k=4 of A292745.
%K A320735 nonn
%O A320735 0,3
%A A320735 _Alois P. Heinz_, Oct 20 2018