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A238640 Position of [n, n, ..., n] (n n's) in Mathematica-ordered list of partitions of n^2.

%I A238640 #29 Feb 20 2020 20:30:30
%S A238640 1,1,3,19,168,1582,15546,157051,1625368,17159223,184277224,2008388660,
%T A238640 22172275440,247558926150,2791793968821,31764451979736,
%U A238640 364283594455091,4207485803818522,48908343969469479,571811846280602486,6720473048598172508,79363083519870386700
%N A238640 Position of [n, n, ..., n] (n n's) in Mathematica-ordered list of partitions of n^2.
%H A238640 Alois P. Heinz, <a href="/A238640/b238640.txt">Table of n, a(n) for n = 0..140</a>
%e A238640 The partitions of 4 in Mathematica order are 4, 31, 22, 211, 1111.  The position of 22 is a(2) = 3.
%p A238640 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A238640       `if`(i<1, 0, b(n, i-1) +`if`(i>n, 0, b(n-i, i))))
%p A238640     end:
%p A238640 a:= n-> 1 +add(b(n^2-j, j), j=n+1..n^2):
%p A238640 seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 03 2014
%t A238640 r[n_] := Table[n, {k, 1, n}]; Flatten[Table[Position[IntegerPartitions[n^2], r[n]], {n, 0, 8}]]
%t A238640 b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1]+If[i>n, 0, b[n-i, i]]]]; a[n_] := 1+Sum[b[n^2-j, j], {j, n+1, n^2}]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Oct 28 2015, after _Alois P. Heinz_ *)
%Y A238640 Cf. A000290, A072213, A080577 (Mathematica ordering), A238638, A238639, A330661, A332706.
%K A238640 nonn
%O A238640 0,3
%A A238640 _Clark Kimberling_, Mar 04 2014
%E A238640 a(9)-a(21) from _Alois P. Heinz_, Sep 03 2014