The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A309386 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A309386

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)

#34 by Joerg Arndt at Fri May 07 05:09:45 EDT 2021

STATUS

reviewed

approved

#33 by Michel Marcus at Fri May 07 04:19:36 EDT 2021

STATUS

proposed

reviewed

#32 by Amiram Eldar at Fri May 07 03:43:28 EDT 2021

STATUS

editing

proposed

#31 by Amiram Eldar at Fri May 07 03:17:03 EDT 2021

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

#30 by Alois P. Heinz at Sun Jul 28 16:48:12 EDT 2019

STATUS

reviewed

approved

#29 by Joerg Arndt at Sun Jul 28 06:25:18 EDT 2019

STATUS

proposed

reviewed

#28 by Seiichi Manyama at Sun Jul 28 04:59:16 EDT 2019

STATUS

editing

proposed

#27 by Seiichi Manyama at Sun Jul 28 00:26:18 EDT 2019

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.

#26 by Seiichi Manyama at Sun Jul 28 00:18:18 EDT 2019

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.

#25 by Seiichi Manyama at Sun Jul 28 00:17:29 EDT 2019

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.

Discussion

Sun Jul 28

00:17

Seiichi Manyama: Formula deformation.