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A025154 Number of partitions of n into distinct parts >= 9.

%I A025154 #16 Nov 24 2020 16:39:50
%S A025154 1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,8,9,10,
%T A025154 12,13,15,17,19,21,24,26,29,33,36,40,45,50,55,62,68,76,84,93,102,114,
%U A025154 125,138,152,168,184,204,223,246,270,297,325,358,391,429,470,515,562,616,672,735
%N A025154 Number of partitions of n into distinct parts >= 9.
%H A025154 Alois P. Heinz, <a href="/A025154/b025154.txt">Table of n, a(n) for n = 0..1000</a>
%F A025154 a(n) = A026829(n+8). - _R. J. Mathar_, Jul 31 2008
%F A025154 G.f.: Product_{j>=9} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A025154 G.f.: Sum_{k>=0} x^(k*(k + 17)/2) / Product_{j=1..k} (1 - x^j). - _Ilya Gutkovskiy_, Nov 24 2020
%p A025154 b:= proc(n, i) option remember;
%p A025154       `if`(n=0, 1, `if`((i-8)*(i+9)/2<n, 0,
%p A025154        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A025154     end:
%p A025154 a:= n-> b(n$2):
%p A025154 seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 07 2014
%t A025154 d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 9 &]; Table[d[n], {n, 25}] (* strict partitions, parts >= 9 *)
%t A025154 Table[Length[d[n]], {n, 40}] (* A025154 for n >= 1 *)
%t A025154 (* _Clark Kimberling_, Mar 07 2014 *)
%Y A025154 Cf. A025147.
%K A025154 nonn
%O A025154 0,20
%A A025154 _Clark Kimberling_