The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A364518

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A364518

Square array read by ascending antidiagonals: T(n,k) = [x^(2*k)] ( (1 + x)^(n+2)/(1 - x)^(n-2) )^k for n, k >= 0.
(history; published version)

#23 by Joerg Arndt at Tue Jul 09 02:21:46 EDT 2024

STATUS

reviewed

approved

#22 by Michel Marcus at Tue Jul 09 01:03:39 EDT 2024

STATUS

proposed

reviewed

#21 by Jason Yuen at Mon Jul 08 21:32:35 EDT 2024

STATUS

editing

proposed

#20 by Jason Yuen at Mon Jul 08 21:32:23 EDT 2024

CROSSREFS

Cf. A000984 (row 0 unsigned), A211419 (row 1 unsigned without 0's), A001448 (row 2), A091496 (row 3), A061162 (row 4), A276098 (row 5), A01448 A001448 bisected (row 6), A276099 (row 7).

STATUS

approved

editing

#19 by Amiram Eldar at Sun Aug 13 07:06:47 EDT 2023

STATUS

reviewed

approved

#18 by Joerg Arndt at Sun Aug 13 03:32:56 EDT 2023

STATUS

proposed

reviewed

#17 by Michel Marcus at Sun Aug 13 03:25:41 EDT 2023

STATUS

editing

proposed

Discussion

Sun Aug 13

03:29

Michel Marcus: antidiagonal

#16 by Michel Marcus at Sun Aug 13 03:25:21 EDT 2023

DATA

1, 1, -2, 1, 0, 6, 1, 6, -10, -20, 1, 16, 70, 0, 70, 1, 30, 630, 924, 198, -252, 1, 48, 2310, 28672, 12870, 0, 924, 1, 70, 6006, 204204, 1385670, 184756, -4420, -3432, 1, 96, 12870, 860160, 19122246, 69206016, 2704156, 0, 12870, 1, 126, 24310, 2704156, 130378950, 1848483780, 3528923580, 40116600, 104006, -48620

PROG

(PARI) T(n, k) = sum(j = 0, 2*k, binomial((n+2)*k, j)*binomial(n*k-j-1, 2*k-j));

lista(nn) = for( n=0, nn, for (k=0, n, print1(T(n-k, k), ", "))); \\ Michel Marcus, Aug 13 2023

STATUS

approved

editing

Discussion

Sun Aug 13

03:25

Michel Marcus: 3 more terms : last row is complete

#15 by Michel Marcus at Sun Aug 13 02:52:52 EDT 2023

STATUS

reviewed

approved

#14 by Joerg Arndt at Sun Aug 13 02:04:38 EDT 2023

STATUS

proposed

reviewed

Discussion

Sun Aug 13

02:52

Michel Marcus: A364519 needs 5 more terms to get last row complete