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A294296
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(Sum_{j>=1} sigma_k(j) * x^j).
3
1, 1, 1, 1, 1, 5, 1, 1, 7, 25, 1, 1, 11, 43, 193, 1, 1, 19, 91, 409, 1481, 1, 1, 35, 223, 1105, 3841, 16021, 1, 1, 67, 595, 3505, 13841, 50431, 167665, 1, 1, 131, 1663, 12193, 60841, 230731, 648187, 2220065, 1, 1, 259, 4771, 44689, 297761, 1340851, 3955771
OFFSET
0,6
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} j*sigma_k(j)*A(n-j,k)/(n-j)! for n > 0.
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
5, 7, 11, 19, 35, ...
25, 43, 91, 223, 595, ...
193, 409, 1105, 3505, 12193, ...
1481, 3841, 13841, 60841, 297761, ...
CROSSREFS
Columns k=0..2 give A294363, A294361, A294362.
Rows n=0-1 give A000012.
Main diagonal gives A294388.
Cf. A144048.
Sequence in context: A299249 A299458 A300096 * A078181 A054110 A132048
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 30 2017
STATUS
approved