A294250 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Product_{j=1..n} (1+x^j) - 1).

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 3, 1, 0, 1, 1, 3, 13, 1, 0, 1, 1, 3, 19, 49, 1, 0, 1, 1, 3, 19, 97, 261, 1, 0, 1, 1, 3, 19, 121, 681, 1531, 1, 0, 1, 1, 3, 19, 121, 921, 5971, 9073, 1, 0, 1, 1, 3, 19, 121, 1041, 8491, 50443, 63393, 1, 0, 1, 1, 3, 19, 121, 1041

Offset

0,13

Links

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

Formula

B(j,k) is the coefficient of Product_{i=1..k} (1+x^i).

A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..min(A000217(k),n)} j*B(j,k)*A(n-j,k)/(n-j)! for n > 0.

Example

Square array A(n,k) begins:
   1, 1,   1,   1,   1, ...
   0, 1,   1,   1,   1, ...
   0, 1,   3,   3,   3, ...
   0, 1,  13,  19,  19, ...
   0, 1,  49,  97, 121, ...
   0, 1, 261, 681, 921, ...

Crossrefs

Columns k=0..5 give A000007, A000012, A118589, A294251, A294252, A294253.

Rows n=0 gives A000012.

Main diagonal gives A293840.

Cf. A070936, A294212, A294254.

Sequence in context: A062719 A305161 A250484 * A117417 A231345 A271344

Adjacent sequences: A294247 A294248 A294249 * A294251 A294252 A294253

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 26 2017

Status

approved