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A160645 A triangular array distributing the values of sequence A120380.

%I A160645 #12 Feb 06 2019 01:57:46
%S A160645 2,5,6,10,55,12,20,302,285,20,36,1307,3216,1015,30,65,4772,24859,
%T A160645 20566,2870,42,110,15509,150264,257954,96000,6930,56,185,46006,763123,
%U A160645 2374064,1834151,360272,14910,72,300,127109,3395312,17535553,24381958
%N A160645 A triangular array distributing the values of sequence A120380.
%C A160645 Column 1 is essentially A000712 and the main diagonal is essentially A002378.
%C A160645 Row n of this triangle is row n*(n+1) of A115994, reversed.
%H A160645 Nathaniel Johnston, <a href="/A160645/b160645.txt">Table of n, a(n) for n = 1..210</a>
%e A160645 The table begins:
%e A160645    2;
%e A160645    5,    6;
%e A160645   10,   55,    12;
%e A160645   20,  302,   285,    20;
%e A160645   36, 1307,  3216,  1015,   30;
%e A160645   65, 4772, 24859, 20566, 2870, 42;
%e A160645   ...
%p A160645 nn:=8: g:=sum(t^k*q^(k^2)/product((1-q^h)^2, h=1..k), k=1..nn): gser:=series(g, q=0, nn*(nn+1)+1): for n from 1 to nn do P[n]:=coeff(gser, q^(n*(n+1))) od: for n from 1 to nn do seq(coeff(P[n], t, n-j+1), j=1..n); od; # _Nathaniel Johnston_, Apr 30 2011
%Y A160645 Cf. A128626 (analogous based on p(n^2)), A000712, A002378.
%K A160645 nonn,tabl
%O A160645 1,1
%A A160645 _Alford Arnold_, May 26 2009
%E A160645 Edited and extended by _Nathaniel Johnston_, Apr 30 2011