cp's OEIS Frontend

A296116 Number of partitions in which each summand, s, may be used with frequency f if f divides s.

%I A296116 #18 Dec 06 2017 07:14:08
%S A296116 1,1,1,2,3,4,4,6,9,12,14,18,23,29,35,43,56,68,82,100,122,147,174,209,
%T A296116 252,302,356,421,500,589,690,808,952,1110,1292,1505,1756,2034,2348,
%U A296116 2715,3139,3620,4156,4778,5492,6296,7195,8220,9398,10714,12194,13872,15784
%N A296116 Number of partitions in which each summand, s, may be used with frequency f if f divides s.
%H A296116 Alois P. Heinz, <a href="/A296116/b296116.txt">Table of n, a(n) for n = 0..10000</a>
%H A296116 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A296116 G.f.: Product_{n >= 1} (1 + Sum_{d divides n} x^(d*n)).
%e A296116 For n=3, the partitions counted are 3 and 2+1.
%e A296116 For n=4: 4, 3+1, 2+2.
%e A296116 For n=5: 5, 4+1, 3+2, 2+2+1.
%p A296116 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1 or n<0, 0,
%p A296116       b(n, i-1)+add(b(n-i*j, i-1), j=numtheory[divisors](i))))
%p A296116     end:
%p A296116 a:= n-> b(n$2):
%p A296116 seq(a(n), n=0..60);  # _Alois P. Heinz_, Dec 05 2017
%t A296116 iend = 30;
%t A296116 s = Series[Product[1 + Sum[x^(Divisors[n][[i]] n), {i, 1, Length[Divisors[n]]}], {n, 1, iend}], {x, 0, iend}]; Print[s];
%t A296116 CoefficientList[s, x]
%Y A296116 Cf. A100471, A100881, A100882, A100883.
%K A296116 nonn
%O A296116 0,4
%A A296116 _David S. Newman_, Dec 04 2017
%E A296116 More terms from _Alois P. Heinz_, Dec 05 2017