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%I #18 Jun 14 2022 15:27:38
%S 1,1,1,1,1,1,2,2,1,1,2,2,1,1,3,4,2,1,3,5,5,3,1,1,4,9,13,13,9,4,1,1,4,
%T 9,13,13,9,4,1,1,5,14,25,30,24,12,3,1,5,15,30,42,42,30,15,5,1,1,6,21,
%U 48,75,81,60,30,10,2
%N Irregular triangle read by rows: rows give the (negated) nonzero coefficients of t in each term of the inverse power product expansion of 1 - t * x/(1-x).
%C Row sums are A290261(n). A regular version is A290320.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 1,
%e 1, 2, 2, 1;
%e 1, 2, 2, 1;
%e 1, 3, 4, 2;
%e 1, 3, 5, 5, 3, 1;
%e 1, 4, 9, 13, 13, 9, 4, 1;
%e 1, 4, 9, 13, 13, 9, 4, 1;
%e 1, 5, 14, 25, 30, 24, 12, 3;
%e 1, 5, 15, 30, 42, 42, 30, 15, 5, 1;
%e 1, 6, 21, 48, 75, 81, 60, 30, 10, 2;
%t eptrees[n_]:=Prepend[Join@@Table[Tuples[eptrees/@y],{y,Rest[IntegerPartitions[n]]}],n];
%t eptrans[a_][n_]:=Sum[(-1)^Count[tree,_List,{0,Infinity}]*Product[a[i],{i,Flatten[{tree}]}],{tree,eptrees[n]}];
%t Table[DeleteCases[CoefficientList[-eptrans[-t&][n],t],0],{n,12}]
%Y Cf. A220418, A273866, A289501, A290261, A290320.
%K tabf,nonn
%O 1,7
%A _Gus Wiseman_, Jul 24 2017
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