A368479 - OEIS

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

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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 A374062 A011075

Adjacent sequences: A368476 A368477 A368478 * A368480 A368481 A368482

KEYWORD

nonn,tabl,easy

AUTHOR

Seiichi Manyama, Dec 26 2023

STATUS

approved