A293461 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} (1 + Sum_{j=1..k} j*x^(j*(2*i-1))).

1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 4, 1, 1, 0, 1, 1, 2, 4, 1, 3, 1, 0, 1, 1, 2, 4, 5, 3, 3, 1, 0, 1, 1, 2, 4, 5, 3, 6, 5, 2, 0, 1, 1, 2, 4, 5, 8, 6, 5, 6, 2, 0, 1, 1, 2, 4, 5, 8, 6, 9, 9, 4, 2, 0, 1, 1, 2, 4, 5, 8, 12, 9, 9, 13

Offset

0,13

Links

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

Example

Square array begins:
   1, 1, 1, 1, 1, ...
   0, 1, 1, 1, 1, ...
   0, 0, 2, 2, 2, ...
   0, 1, 1, 4, 4, ...
   0, 1, 1, 1, 5, ...
   0, 1, 3, 3, 3, ...

Mathematica

max = 12; A[n_, k_] := SeriesCoefficient[Product[(x*(-(k*x^((2*i - 1)*(k + 1) + 1)) - x^((2*i - 1)*(k + 1) + 1) + k*x^((2*i - 1)*(k + 1) + 2*i) + x^(2*i)))/(x^(2*i) - x)^2 + 1, {i, 1, max}], {x, 0, n}]; Flatten[ Table[ A[n - k, k], {n, 0, max}, {k, n, 0, -1}]] (* Jean-François Alcover, Oct 10 2017 *)

Crossrefs

Columns k=0..3 give A000007, A000700, A293304, A293463.

Rows n=0..1 give A000012, A057427.

Main diagonal gives A102186.

Cf. A290216.

Sequence in context: A037897 A190248 A054070 * A255482 A204172 A126304

Adjacent sequences: A293458 A293459 A293460 * A293462 A293463 A293464

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 09 2017

Status

approved