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.

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

Links

Table of n, a(n) for n=0..65.

OEIS Wiki, Eulerian polynomials.

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.

Cf. A173018, A303990, A368479.

Sequence in context: A346415 A362894 A352067 * A178245 A338753 A167666

Adjacent sequences: A368483 A368484 A368485 * A368487 A368488 A368489

Keyword

nonn,tabl,easy

Author

Seiichi Manyama, Dec 26 2023

Status

approved