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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)).
4
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
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.
Sequence in context: A298739 A346366 A325011 * A331956 A325019 A152151
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 24 2017
STATUS
approved