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, 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.

Links

Table of n, a(n) for n=1..78.

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

Cf. A220418, A273866, A289501, A290261, A290262.

Sequence in context: A139352 A214039 A089679 * A348761 A318703 A332384

Adjacent sequences: A290317 A290318 A290319 * A290321 A290322 A290323

Keyword

nonn,tabl

Author

Gus Wiseman, Jul 27 2017

Status

approved