A293525 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. Product_{j > 0, j mod k > 0} exp(x^j).

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 3, 7, 0, 1, 1, 3, 7, 25, 0, 1, 1, 3, 13, 49, 181, 0, 1, 1, 3, 13, 49, 321, 1201, 0, 1, 1, 3, 13, 73, 381, 2131, 10291, 0, 1, 1, 3, 13, 73, 381, 2971, 19783, 97777, 0, 1, 1, 3, 13, 73, 501, 3331, 26713, 195777, 1013545, 0, 1, 1

Offset

0,13

Links

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

Formula

E.g.f. of column k: exp((Sum_{j=1..k-1} x^j)/(1 - x^k)).

Example

Square array begins:
   1,   1,   1,   1,   1, ...
   0,   1,   1,   1,   1, ...
   0,   1,   3,   3,   3, ...
   0,   7,   7,  13,  13, ...
   0,  25,  49,  49,  73, ...
   0, 181, 321, 381, 381, ...

Mathematica

kmax = 12; col[k_] := PadRight[(Exp[Sum[x^j, {j, 1, k - 1}]/(1 - x^k)] + O[x]^kmax // CoefficientList[#, x] &), kmax]*Range[0, kmax - 1]!; A = Array[col, kmax]; Table[A[[n - k + 1, k]], {n, 1, kmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 12 2017, from formula *)

Crossrefs

Columns k=1..3 give A000007, A088009, A113775.

Rows n=0 gives A000012.

Main diagonal gives A000262.

Cf. A293530.

Sequence in context: A222010 A152590 A261873 * A016617 A299632 A249186

Adjacent sequences: A293522 A293523 A293524 * A293526 A293527 A293528

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 11 2017

Status

approved