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A290320
Write 1 - t * x/(1-x) as an inverse power product 1/(1+c(1)x) * 1/(1+c(2)x^2) * 1/(1+c(3)x^3) * ... The sequence is a regular triangle where T(n,k) is the coefficient of t^k in c(n), 1 <= k <= n.
1
1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 2, 1, 0, 1, 3, 4, 2, 0, 0, 1, 3, 5, 5, 3, 1, 0, 1, 4, 9, 13, 13, 9, 4, 1, 1, 4, 9, 13, 13, 9, 4, 1, 0, 1, 5, 14, 25, 30, 24, 12, 3, 0, 0, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 0, 1, 6, 21, 48, 75, 81, 60, 30, 10, 2, 0, 0
OFFSET
1,8
COMMENTS
An irregular triangle with only the nonzero coefficients is given by A290262.
EXAMPLE
Triangle begins:
1;
1, 1;
1, 1, 0;
1, 2, 2, 1;
1, 2, 2, 1, 0;
1, 3, 4, 2, 0, 0;
1, 3, 5, 5, 3, 1, 0;
1, 4, 9, 13, 13, 9, 4, 1;
1, 4, 9, 13, 13, 9, 4, 1, 0;
1, 5, 14, 25, 30, 24, 12, 3, 0, 0;
1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 0;
1, 6, 21, 48, 75, 81, 60, 30, 10, 2, 0, 0;
MATHEMATICA
nn=12; Solve[Table[Expand[SeriesCoefficient[Product[1/(1+c[k]x^k), {k, n}], {x, 0, n}]]==-t, {n, nn}], Table[c[n], {n, nn}]][[1, All, 2]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Jul 27 2017
STATUS
approved