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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).
6
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
1,7
COMMENTS
Row sums are A290261(n). A regular version is A290320.
EXAMPLE
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;
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}]
CROSSREFS
KEYWORD
tabf,nonn
AUTHOR
Gus Wiseman, Jul 24 2017
STATUS
approved