A292477 Square array A(n,k), n >= 0, k >= 2, read by antidiagonals: A(n,k) = [x^(k*n)] Product_{j>=0} 1/(1 - x^(k^j)).

1, 1, 2, 1, 2, 4, 1, 2, 3, 6, 1, 2, 3, 5, 10, 1, 2, 3, 4, 7, 14, 1, 2, 3, 4, 6, 9, 20, 1, 2, 3, 4, 5, 8, 12, 26, 1, 2, 3, 4, 5, 7, 10, 15, 36, 1, 2, 3, 4, 5, 6, 9, 12, 18, 46, 1, 2, 3, 4, 5, 6, 8, 11, 15, 23, 60, 1, 2, 3, 4, 5, 6, 7, 10, 13, 18, 28, 74, 1, 2, 3, 4, 5, 6, 7, 9, 12, 15, 21, 33, 94

Offset

0,3

Comments

A(n,k) is the number of partitions of k*n into powers of k.

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

George E. Andrews, Aviezri S. Fraenkel, James A. Sellers, Characterizing the number of m-ary partitions modulo m, Amer. Math. Monthly 122:9 (2015), 880-885.

Index entries for related partition-counting sequences

Example

Square array begins:
   1,  1,  1,  1,  1,  1, ...
   2,  2,  2,  2,  2,  2, ...
   4,  3,  3,  3,  3,  3, ...
   6,  5,  4,  4,  4,  4, ...
  10,  7,  6,  5,  5,  5, ...
  14,  9,  8,  7,  6,  6, ...

Mathematica

Table[Function[k, SeriesCoefficient[Product[1/(1 - x^k^i), {i, 0, n}], {x, 0, k n}]][j - n + 2], {j, 0, 12}, {n, 0, j}] // Flatten

Crossrefs

Columns k=2..5 give A000123, A005704, A005705, A005706.

Mirror of A089688 (excluding the first row).

Cf. A145515, A294316.

Sequence in context: A081517 A104778 A356184 * A081532 A174843 A253572

Adjacent sequences: A292474 A292475 A292476 * A292478 A292479 A292480

Keyword

nonn,tabl

Author

Ilya Gutkovskiy, Sep 17 2017

Status

approved