A333925 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j=2..k+1} 1/(1 - x^j).

1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 0, 1, 0, 1, 1, 2, 2, 3, 1, 1, 0, 1, 0, 1, 1, 2, 2, 3, 2, 2, 0, 0, 1, 0, 1, 1, 2, 2, 4, 3, 4, 2, 1, 0, 1, 0, 1, 1, 2, 2, 4, 3, 5, 3, 2, 0, 0, 1, 0, 1, 1, 2, 2, 4, 4, 6, 5, 5, 2, 1, 0

Offset

0,33

Comments

A(n,k) is the number of partitions of n into parts 2, 3, ..., k and k + 1.

Links

David A. Corneth, Table of n, a(n) for n = 0..10010 (first 141 rows antidiagonals flattened)

Index entries for Molien series

Formula

G.f. of column k: Product_{j=2..k+1} 1/(1 - x^j).

Example

Square array begins:
  1,  1,  1,  1,  1,  1,  ...
  0,  0,  0,  0,  0,  0,  ...
  0,  1,  1,  1,  1,  1,  ...
  0,  0,  1,  1,  1,  1,  ...
  0,  1,  1,  2,  2,  2,  ...
  0,  0,  1,  1,  2,  2,  ...

Mathematica

Table[Function[k, SeriesCoefficient[Product[1/(1 - x^j), {j, 2, k + 1}], {x, 0, n}]][i - n], {i, 0, 13}, {n, 0, i}] // Flatten

Crossrefs

Columns k=0..12 give A000007, A059841, A103221, A266755, A008667, A037145, A001996, A266776, A266777, A266778, A266779, A266780, A266781.

Main diagonal gives A002865.

Cf. A008284, A058398.

Sequence in context: A194821 A044934 A124761 * A342595 A156709 A081400

Adjacent sequences: A333922 A333923 A333924 * A333926 A333927 A333928

Keyword

nonn,tabl

Author

Ilya Gutkovskiy, Apr 10 2020

Status

approved