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A368486
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^j * j^k.
3
1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 3, 18, 6, 1, 0, 4, 75, 90, 10, 1, 0, 5, 260, 804, 346, 15, 1, 0, 6, 805, 5444, 5988, 1146, 21, 1, 0, 7, 2310, 31180, 70980, 36363, 3450, 28, 1, 0, 8, 6279, 159774, 671180, 710980, 193827, 9722, 36, 1, 0, 9, 16392, 756420, 5468190, 10436805, 6019396, 943968, 26106, 45, 1
OFFSET
0,8
FORMULA
G.f. of column k: k*x*A_k(k*x)/((1-x) * (1-k*x)^(k+1)), where A_n(x) are the Eulerian polynomials for k > 0.
EXAMPLE
Square array begins:
1, 0, 0, 0, 0, 0, ...
1, 1, 2, 3, 4, 5, ...
1, 3, 18, 75, 260, 805, ...
1, 6, 90, 804, 5444, 31180, ...
1, 10, 346, 5988, 70980, 671180, ...
1, 15, 1146, 36363, 710980, 10436805, ...
PROG
(PARI) T(n, k) = sum(j=0, n, k^j*j^k);
CROSSREFS
Columns k=0..3 give A000012, A000217, A036800, A343808.
Main diagonal gives A303991.
Sequence in context: A346415 A362894 A352067 * A178245 A338753 A167666
KEYWORD
nonn,tabl,easy
AUTHOR
Seiichi Manyama, Dec 26 2023
STATUS
approved