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A349706
Array T(n,k) = Sum_{j=0, k} binomial(k,j)*j^n for n and k >= 0, read by ascending antidiagonals.
0
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
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
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Nov 26 2021
STATUS
approved