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A128626 A triangular array distributing the values of sequence A072213 (cf. A115994).

%I A128626 #7 Feb 06 2019 00:25:07
%S A128626 1,4,1,9,20,1,16,140,74,1,25,572,1136,224,1,36,1785,8866,6685,604,1,
%T A128626 49,4600,47152,88380,31851,1492,1,64,10416,194282,737059,665542,
%U A128626 130808,3458,1,81,21320,665769,4512584,8211274,4105870,479826,7602,1,100,40425
%N A128626 A triangular array distributing the values of sequence A072213 (cf. A115994).
%H A128626 Nathaniel Johnston, <a href="/A128626/b128626.txt">Table of n, a(n) for n = 0..209</a>
%e A128626 A115994 distributes the numeric partition sequence A000041 and A072213 records partition values for sequence A000290 (the squares).
%e A128626 Therefore the table begins:
%e A128626    1;
%e A128626    4,    1;
%e A128626    9,   20,     1;
%e A128626   16,  140,    74,     1;
%e A128626   25,  572,  1136,   224,     1;
%e A128626   36, 1785,  8866,  6685,   604,    1;
%e A128626   49, 4600, 47152, 88380, 31851, 1492, 1;
%e A128626   ...
%p A128626 nn:=8: g:=sum(t^k*q^(k^2)/product((1-q^j)^2, j=1..k), k=1..nn): gser:=series(g, q=0, nn^2+1): for n from 1 to nn do P[n]:=coeff(gser, q^(n^2)) od: for n from 1 to nn do seq(coeff(P[n], t^j), j=1..n); od; # _Nathaniel Johnston_, Apr 30 2011
%Y A128626 Cf. A000041, A000290, A115994.
%K A128626 nonn,tabl
%O A128626 0,2
%A A128626 _Alford Arnold_, Mar 15 2007