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A361652
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} k^j * Stirling2(n-j,j)/(n-j)!.
1
1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 4, 3, 0, 1, 0, 6, 6, 16, 0, 1, 0, 8, 9, 56, 65, 0, 1, 0, 10, 12, 120, 250, 336, 0, 1, 0, 12, 15, 208, 555, 1812, 1897, 0, 1, 0, 14, 18, 320, 980, 5148, 12614, 11824, 0, 1, 0, 16, 21, 456, 1525, 11064, 39711, 101040, 80145, 0
OFFSET
0,9
FORMULA
E.g.f. of column k: exp(k * x * (exp(x) - 1)).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 0, 0, 0, 0, 0, ...
0, 2, 4, 6, 8, 10, ...
0, 3, 6, 9, 12, 15, ...
0, 16, 56, 120, 208, 320, ...
0, 65, 250, 555, 980, 1525, ...
PROG
(PARI) T(n, k) = n!*sum(j=0, n\2, k^j*stirling(n-j, j, 2)/(n-j)!);
CROSSREFS
Columns k=0..3 give: A000007, A052506, A351733, A351734.
Main diagonal gives (-1)^n * A290158(n).
Cf. A362834.
Sequence in context: A134317 A123641 A217377 * A362834 A362839 A362837
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, May 05 2023
STATUS
approved