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A357320 The total number of fixed points among all strict partitions of n, when parts are written in increasing order.

%I A357320 #25 Sep 30 2022 03:50:31
%S A357320 0,1,0,2,1,1,4,3,4,4,9,8,11,12,15,21,24,28,34,40,46,60,67,80,93,110,
%T A357320 125,148,174,200,231,268,306,354,404,461,534,606,690,786,895,1012,
%U A357320 1150,1298,1467,1662,1872,2104,2374,2664,2990,3355,3759,4202,4702,5256
%N A357320 The total number of fixed points among all strict partitions of n, when parts are written in increasing order.
%C A357320 For instance, the partition (1,2,4,7,11) = (y(1),y(2),y(3),y(4),y(5)) has 2 fixed points, since y(1) = 1 and y(2) = 2.
%F A357320 G.f.: (Product_{k>=1}(1+q^k))*Sum_{n>=1}q^(n*(n+1)/2)/Product_{k=1..n}(1+q^k).
%e A357320 The 10 strict partition of 10 are (1,2,3,4), (2,3,5), (1,4,5), (1,3,6), (4,6), (1,2,7), (3,7), (2,8), (1,9), and (10), containing 4,0,1,1,0,2,0,0,1, and 0 fixed points, respectively, and so a(10) = 9.
%Y A357320 For the same count but where parts are written in decreasing order, see A352829.
%Y A357320 For the case of ordinary partitions, see A357459.
%K A357320 nonn
%O A357320 0,4
%A A357320 _Jeremy Lovejoy_, Sep 29 2022