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A293785
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} j^(k-1)*x^j).
2
1, 1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 1, 5, 13, 24, 1, 1, 9, 31, 73, 120, 1, 1, 17, 79, 241, 501, 720, 1, 1, 33, 211, 841, 2261, 4051, 5040, 1, 1, 65, 583, 3049, 10821, 24781, 37633, 40320, 1, 1, 129, 1651, 11353, 54221, 162601, 309835, 394353, 362880, 1, 1, 257
OFFSET
0,6
LINKS
FORMULA
A(0,k) = 1 and A(n,k) = (n-1)! * Sum_{j=1..n} j^k*A(n-j,k)/(n-j)! for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
2, 3, 5, 9, 17, ...
6, 13, 31, 79, 211, ...
24, 73, 241, 841, 3049, ...
120, 501, 2261, 10821, 54221, ...
CROSSREFS
Columns k=0..4 give A000142, A000262, A082579, A255807, A255819.
Rows n=0-1 give A000012.
Main diagonal gives A293786.
Sequence in context: A156540 A156582 A156953 * A156881 A376554 A056646
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 16 2017
STATUS
approved