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Revision History for A365674

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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Triangle read by rows. T(n, k) = ((n - k + 1)*(n - k + 2)/2) * T(n, k - 1) + T(n - 1, k) for 0 < k < n, T(n, 0) = 1 and T(n, n) = T(n, n - 1) for n > 0.
(history; published version)

#7 by Michael De Vlieger at Sat Sep 30 20:58:06 EDT 2023

STATUS

proposed

approved

#6 by Peter Luschny at Sat Sep 30 17:21:32 EDT 2023

STATUS

editing

proposed

#5 by Peter Luschny at Sat Sep 30 17:15:29 EDT 2023

NAME

Triangle read by rows. T(n, k) = ((n - k + 1)*(n - k + 2)/2) * T(n, k - 1) + T(n - 1, k) for 0 < k < n, T(n, 0) = 1 and T(n, n) = T(n, n - 1) for n > 0.

COMMENTS

This triangle is associated to the case n = 3 of A365673 and has as weight function the triangular numbers A000217. The numbers on its main diagonal are the reduced tangent numbers A002105. For details see A365673.

CROSSREFS

Cf. A002105 (main diagonal), A365673 (case n=3), A000217 (weight).

#4 by Peter Luschny at Sat Sep 30 11:45:55 EDT 2023

MAPLE

T := proc(n, k) option remember; if k = 0 then 1 else if k = n then T(n, k - 1) else ((n - k + 1)*(n - k + 2)/2) * T( n, k - 1) + T( n - 1, k) fi fi end:

seq(print(seq(T(n, k), k = 0..n)), n = 0..8);

CROSSREFS

Cf. A002105 (main diagonal), A365673 (case n=3).

#3 by Peter Luschny at Sat Sep 30 11:17:57 EDT 2023

NAME

allocated for Peter LuschnyTriangle read by rows.

DATA

1, 1, 1, 1, 4, 4, 1, 10, 34, 34, 1, 20, 154, 496, 496, 1, 35, 504, 3520, 11056, 11056, 1, 56, 1344, 16960, 112816, 349504, 349504, 1, 84, 3108, 63580, 748616, 4841200, 14873104, 14873104, 1, 120, 6468, 199408, 3739736, 42238560, 268304464, 819786496, 819786496

OFFSET

0,5

EXAMPLE

[0] 1;

[1] 1, 1;

[2] 1, 4, 4;

[3] 1, 10, 34, 34;

[4] 1, 20, 154, 496, 496;

[5] 1, 35, 504, 3520, 11056, 11056;

[6] 1, 56, 1344, 16960, 112816, 349504, 349504;

[7] 1, 84, 3108, 63580, 748616, 4841200, 14873104, 14873104;

CROSSREFS

Cf. A002105 (main diagonal).

KEYWORD

allocated

nonn,tabl

AUTHOR

Peter Luschny, Sep 30 2023

STATUS

approved

editing

#2 by Peter Luschny at Fri Sep 15 05:11:26 EDT 2023

KEYWORD

allocating

allocated

#1 by Peter Luschny at Fri Sep 15 05:11:26 EDT 2023

NAME

allocated for Peter Luschny

KEYWORD

allocating

STATUS

approved