A290262 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).

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, 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, 48, 75, 81, 60, 30, 10, 2

Offset: 1

Author

Gus Wiseman, Jul 24 2017

Keywords

• tabf
• nonn

Comments

Row sums are A290261(n). A regular version is A290320.

Examples

			Triangle begins:
  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,  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, 48, 75, 81, 60, 30, 10,  2;
		

Crossrefs

Cf. A220418, A273866, A289501, A290261, A290320.

Programs

Mathematica

eptrees[n_]:=Prepend[Join@@Table[Tuples[eptrees/@y],{y,Rest[IntegerPartitions[n]]}],n];
eptrans[a_][n_]:=Sum[(-1)^Count[tree,_List,{0,Infinity}]*Product[a[i],{i,Flatten[{tree}]}],{tree,eptrees[n]}];
Table[DeleteCases[CoefficientList[-eptrans[-t&][n],t],0],{n,12}]