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A320741 Number of partitions of n with ten sorts of part 1 which are introduced in ascending order.

%I A320741 #8 Dec 07 2020 09:03:45
%S A320741 1,1,3,7,20,63,233,966,4454,22404,121616,706361,4361910,28491982,
%T A320741 196018395,1414922459,10677120529,83924901635,684582037213,
%U A320741 5772723290503,50123602905429,446382776341382,4062023996661972,37638652689027910,354017801203414670
%N A320741 Number of partitions of n with ten sorts of part 1 which are introduced in ascending order.
%H A320741 Alois P. Heinz, <a href="/A320741/b320741.txt">Table of n, a(n) for n = 0..1006</a>
%p A320741 b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
%p A320741       Stirling2(n, j), j=0..10), add(b(n-i*j, i-1), j=0..n/i))
%p A320741     end:
%p A320741 a:= n-> b(n$2):
%p A320741 seq(a(n), n=0..40);
%t A320741 b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 10}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
%t A320741 a[n_] := b[n, n];
%t A320741 a /@ Range[0, 40] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A320741 Column k=10 of A292745.
%K A320741 nonn
%O A320741 0,3
%A A320741 _Alois P. Heinz_, Oct 20 2018