A368479 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} 2^j * j^k.

1, 0, 3, 0, 2, 7, 0, 2, 10, 15, 0, 2, 18, 34, 31, 0, 2, 34, 90, 98, 63, 0, 2, 66, 250, 346, 258, 127, 0, 2, 130, 714, 1274, 1146, 642, 255, 0, 2, 258, 2074, 4810, 5274, 3450, 1538, 511, 0, 2, 514, 6090, 18458, 24810, 19098, 9722, 3586, 1023

Offset

0,3

Links

Table of n, a(n) for n=0..54.

OEIS Wiki, Eulerian polynomials.

Formula

G.f. of column k: 2*x*A_k(2*x)/((1-x) * (1-2*x)^(k+1)), where A_n(x) are the Eulerian polynomials for k > 0.

Example

Square array begins:
    1,   0,    0,     0,      0,      0,       0, ...
    3,   2,    2,     2,      2,      2,       2, ...
    7,  10,   18,    34,     66,    130,     258, ...
   15,  34,   90,   250,    714,   2074,    6090, ...
   31,  98,  346,  1274,   4810,  18458,   71626, ...
   63, 258, 1146,  5274,  24810, 118458,  571626, ...
  127, 642, 3450, 19098, 107754, 616122, 3557610, ...

Prog

(PARI) T(n, k) = sum(j=0, n, 2^j*j^k);

Crossrefs

Columns k=0..3 give A126646, A036799, A036800, A036827.

Main diagonal gives A368466.

Cf. A103438, A173018, A368486.

Sequence in context: A274417 A208764 A209129 * A282694 A011075 A248820

Adjacent sequences: A368476 A368477 A368478 * A368480 A368481 A368482

Keyword

nonn,tabl,easy

Author

Seiichi Manyama, Dec 26 2023

Status

approved