The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A369134

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A369134

Triangle read by rows: T(n, k) = (-1)^(n + 1)*L(n) * M(n, k) where M is the inverse of the matrix generated by the triangle A368846 and L(n) is the lcm of the denominators of the terms in the n-th row of M.
(history; published version)

#23 by Peter Luschny at Mon Jan 15 10:02:00 EST 2024

STATUS

proposed

approved

#22 by Paolo Xausa at Mon Jan 15 09:18:03 EST 2024

STATUS

editing

proposed

Discussion

Mon Jan 15

10:01

Peter Luschny: Thank you!

#21 by Paolo Xausa at Mon Jan 15 09:17:20 EST 2024

MATHEMATICA

Map[# Apply[LCM, @@ Denominator[#]]&, MapIndexed[(-1)^First[#2] Take[#, First[#2]]&, Inverse[PadRight[Table[A368846[n, k], {n, 0, 10}, {k, 0, n}]]]]] (* Paolo Xausa, Jan 15 2024 *)

#20 by Paolo Xausa at Mon Jan 15 09:13:31 EST 2024

MATHEMATICA

A368846[n_, k_] := If[k == 0, Boole[n == 0], (-1)^(n + k) 2 Binomial[2 k - 1, n] Binomial[2 n + 1, 2 k]];

Map[# Apply[LCM, Denominator[#]]&, MapIndexed[(-1)^First[#2] Take[#, First[#2]]&, Inverse[PadRight[Table[A368846[n, k], {n, 0, 10}, {k, 0, n}]]]]] (* Paolo Xausa, Jan 15 2024 *)

STATUS

approved

editing

#19 by Peter Luschny at Mon Jan 15 06:58:51 EST 2024

STATUS

editing

approved

#18 by Peter Luschny at Mon Jan 15 06:58:16 EST 2024

DATA

-1, 0, 1, 0, 0, -1, 0, 0, 7, 3, 0, 0, -14, -6, -1, 0, 0, 693, 297, 55, 5, 0, 0, -30030, -12870, -2431, -260, -15, 0, 0, 4150146, 1778634, 337480, 37310, 2625, 105, 0, 0, -21441420, -9189180, -1745458, -194480, -14280, -714, -21

EXAMPLE

[0] [-1]

STATUS

approved

editing

#17 by Peter Luschny at Mon Jan 15 06:49:39 EST 2024

STATUS

editing

approved

#16 by Peter Luschny at Mon Jan 15 06:48:25 EST 2024

NAME

Triangle read by rows: T(n, k) = (-1)^(n + 1)*L(n) * M(n, k) where M is the inverse of the matrix generated by the triangle A368846 and L(n) is the lcm of the denominators of the terms in the n-th row of M.

STATUS

approved

editing

Discussion

Mon Jan 15

06:49

Peter Luschny: As Paolo Xausa rightly observed we have to adjust also the name. Thanks Paolo!

#15 by Peter Luschny at Mon Jan 15 04:49:44 EST 2024

STATUS

editing

approved

#14 by Peter Luschny at Mon Jan 15 04:49:17 EST 2024

PROG

L = (-1)**(n + 1)*lcm(M[n][k].denominator() for k in range(n + 1))

STATUS

approved

editing

Discussion

Mon Jan 15

04:49

Peter Luschny: Sign correction.