cp's OEIS Frontend

A320738 Number of partitions of n with seven sorts of part 1 which are introduced in ascending order.

%I A320738 #8 Dec 07 2020 09:04:40
%S A320738 1,1,3,7,20,63,233,966,4453,22367,120819,693233,4178068,26179581,
%T A320738 169020426,1115994109,7491323062,50893512269,348746702822,
%U A320738 2404544709055,16651752622351,115675136440751,805342277995251,5615683405472021,39202038270665250,273878789880840798
%N A320738 Number of partitions of n with seven sorts of part 1 which are introduced in ascending order.
%H A320738 Alois P. Heinz, <a href="/A320738/b320738.txt">Table of n, a(n) for n = 0..1187</a>
%p A320738 b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
%p A320738       Stirling2(n, j), j=0..7), add(b(n-i*j, i-1), j=0..n/i))
%p A320738     end:
%p A320738 a:= n-> b(n$2):
%p A320738 seq(a(n), n=0..40);
%t A320738 b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 7}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
%t A320738 a[n_] := b[n, n];
%t A320738 a /@ Range[0, 40] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A320738 Column k=7 of A292745.
%K A320738 nonn
%O A320738 0,3
%A A320738 _Alois P. Heinz_, Oct 20 2018