A349706 Array T(n,k) = Sum_{j=0, k} binomial(k,j)*j^n for n and k >= 0, read by ascending antidiagonals.

1, 0, 2, 0, 1, 4, 0, 1, 4, 8, 0, 1, 6, 12, 16, 0, 1, 10, 24, 32, 32, 0, 1, 18, 54, 80, 80, 64, 0, 1, 34, 132, 224, 240, 192, 128, 0, 1, 66, 342, 680, 800, 672, 448, 256, 0, 1, 130, 924, 2192, 2880, 2592, 1792, 1024, 512, 0, 1, 258, 2574, 7400, 11000, 10752, 7840, 4608, 2304, 1024

Offset

0,3

Links

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

Renate Golombek, Aufgabe 1088, El. Math., 49 (1994), 126-127.

Simsek Yilmaz, New families of special numbers for computing negative order Euler numbers and related numbers and polynomials, Applicable Analysis and Discrete Mathematics 2018 Volume 12, Issue 1, Pages: 1-35. See B(n,k).

Example

Array begins:
  1 2  4   8   16    32
  0 1  4  12   32    80
  0 1  6  24   80   240
  0 1 10  54  224   800
  0 1 18 132  680  2880
  0 1 34 342 2192 11000

Mathematica

T[n_, k_] := Sum[Binomial[k, j] * If[j == n == 0, 1, j^n], {j, 0, k}]; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Nov 26 2021 *)

Prog

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

Crossrefs

Cf. A000079 (row 0), A001787 (row 1), A001788 (row 2), A058645 (row 3), A058649 (row 4), A059338 (row 5), A056468 (row 6), A084641 (row 7).

Sequence in context: A208756 A259873 A121462 * A271466 A218581 A307177

Adjacent sequences: A349703 A349704 A349705 * A349707 A349708 A349709

Keyword

nonn,tabl

Author

Michel Marcus, Nov 26 2021

Status

approved