The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A306245 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A306245

Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = Sum_{j=0..n-1} k^j * binomial(n-1,j) * A(j,k) for n > 0.
(history; published version)

#79 by Michael De Vlieger at Sat Jun 18 23:03:43 EDT 2022

STATUS

proposed

approved

#78 by Seiichi Manyama at Sat Jun 18 14:25:25 EDT 2022

STATUS

editing

proposed

#77 by Seiichi Manyama at Sat Jun 18 14:25:22 EDT 2022

CROSSREFS

Columns k=0..2 4 give A000012, A000110, A126443, A355081, A355082.

STATUS

approved

editing

#76 by N. J. A. Sloane at Sat Jun 18 13:59:35 EDT 2022

STATUS

proposed

approved

#75 by Seiichi Manyama at Sat Jun 18 11:19:08 EDT 2022

STATUS

editing

proposed

#74 by Seiichi Manyama at Sat Jun 18 11:18:34 EDT 2022

FORMULA

gG.f. A_k(x) of column k satisfies A_k(x) = 1 + x * A_k(k * x / (1 - x)) / (1 - x). - Seiichi Manyama, Jun 18 2022

#73 by Seiichi Manyama at Sat Jun 18 11:17:50 EDT 2022

FORMULA

E.g.f. A_k(x) of column k satisfies A_k(x) = 1 + x * A_k(k * x / (1 - x)) / (1 - x). - Seiichi Manyama, Jun 18 2022

STATUS

proposed

editing

#72 by Seiichi Manyama at Sat Jun 18 11:16:35 EDT 2022

STATUS

editing

proposed

#71 by Seiichi Manyama at Sat Jun 18 11:15:52 EDT 2022

FORMULA

E.g.f. A_k(x) of column k A_k(x) satisfies A_k(x) = 1 + x * A_k(k * x / (1 - x)) / (1 - x). - Seiichi Manyama, Jun 18 2022

#70 by Seiichi Manyama at Sat Jun 18 11:13:02 EDT 2022

FORMULA

E.g.f. of column k A_k(x) satisfies A_k(x) = 1 + x * A_k(k * x / (1 - x)) / (1 - x). - _Seiichi Manyama_, Jun 18 2022