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A320737 Number of partitions of n with six sorts of part 1 which are introduced in ascending order.

%I A320737 #8 Dec 07 2020 09:03:27
%S A320737 1,1,3,7,20,63,233,965,4425,21904,114910,628754,3544272,20393306,
%T A320737 118986963,700768255,4152987416,24714368292,147480695339,881688073414,
%U A320737 5277421580515,31613933962624,189481916086717,1136086826214117,6813308511956936,40867019987219945
%N A320737 Number of partitions of n with six sorts of part 1 which are introduced in ascending order.
%H A320737 Alois P. Heinz, <a href="/A320737/b320737.txt">Table of n, a(n) for n = 0..1288</a>
%p A320737 b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
%p A320737       Stirling2(n, j), j=0..6), add(b(n-i*j, i-1), j=0..n/i))
%p A320737     end:
%p A320737 a:= n-> b(n$2):
%p A320737 seq(a(n), n=0..40);
%t A320737 b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 6}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
%t A320737 a[n_] := b[n, n];
%t A320737 a /@ Range[0, 40] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A320737 Column k=6 of A292745.
%K A320737 nonn
%O A320737 0,3
%A A320737 _Alois P. Heinz_, Oct 20 2018