STATUS
reviewed
approved
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Revision History for A309386
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(n,k) = Sum_{j=0..n} (-k)^(n-j)*Stirling2(n,j).
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
MATHEMATICA
T[n_, k_] := Sum[If[k == n-j == 0, 1, (-k)^(n-j)] * StirlingS2[n, j], {j, 0, n}]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 07 2021 *)
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
FORMULA
A(0,k) = 1 and A(n,k) = Sum_{j=0..n-1} (-k)^(n-1-j) * binomial(n-1,j) * A(j,k) for n > 0.
FORMULA
A(0,k) = 1 and A(n,k) = -k * Sum_{j=0..n-1} (-k)^(n-j) * binomial(n-1,j) * A(j,k) for n > 0.
FORMULA
A(0,k) = 1 and A(n,k) = -k * Sum_{j=10..n-1} (-k)^(n-j-1) * binomial(n-1,j-1) * A(n-j,k) for n > 0.