A349706 Square 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
Examples
Square 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
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
- 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).
Crossrefs
Programs
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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 *) -
PARI
T(n,k) = sum(j=0, k, binomial(k,j)*j^n);