A294188 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(k*(1/(1-x)^k - 1)).

1, 1, 0, 1, 1, 0, 1, 4, 3, 0, 1, 9, 28, 13, 0, 1, 16, 117, 256, 73, 0, 1, 25, 336, 1881, 2848, 501, 0, 1, 36, 775, 8416, 35505, 37024, 4051, 0, 1, 49, 1548, 27925, 241696, 763209, 547936, 37633, 0, 1, 64, 2793, 75888, 1134025, 7769856, 18309861, 9064192

Offset

0,8

Links

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

Formula

A(0,k) = 1 and A(n,k) = k^2 * (n-1)! * Sum_{j=1..n} binomial(j+k-1,k)*A(n-j,k)/(n-j)! for n > 0.

Example

Square array A(n,k) begins:
   1,   1,     1,      1,       1, ...
   0,   1,     4,      9,      16, ...
   0,   3,    28,    117,     336, ...
   0,  13,   256,   1881,    8416, ...
   0,  73,  2848,  35505,  241696, ...
   0, 501, 37024, 763209, 7769856, ...

Crossrefs

Columns k=0..3 give A000007, A000262, A294189, A294190.

Rows n=0..1 give A000012, A000290.

Main diagonal gives A294192.

Cf. A291709, A294046.

Sequence in context: A298739 A346366 A325011 * A331956 A325019 A152151

Adjacent sequences: A294185 A294186 A294187 * A294189 A294190 A294191

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 24 2017

Status

approved