A360859 - OEIS

A360859

Triangle read by rows. T(n, k) = binomial(n, ceil(k/2)) * binomial(n, floor(k/2)).

1, 1, 1, 1, 2, 4, 1, 3, 9, 9, 1, 4, 16, 24, 36, 1, 5, 25, 50, 100, 100, 1, 6, 36, 90, 225, 300, 400, 1, 7, 49, 147, 441, 735, 1225, 1225, 1, 8, 64, 224, 784, 1568, 3136, 3920, 4900, 1, 9, 81, 324, 1296, 3024, 7056, 10584, 15876, 15876, 1, 10, 100, 450, 2025, 5400, 14400, 25200, 44100, 52920, 63504

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

Triangle T(n, k) starts:

[0] 1;

[1] 1, 1;

[2] 1, 2, 4;

[3] 1, 3, 9, 9;

[4] 1, 4, 16, 24, 36;

[5] 1, 5, 25, 50, 100, 100;

[6] 1, 6, 36, 90, 225, 300, 400;

[7] 1, 7, 49, 147, 441, 735, 1225, 1225;

[8] 1, 8, 64, 224, 784, 1568, 3136, 3920, 4900;

[9] 1, 9, 81, 324, 1296, 3024, 7056, 10584, 15876, 15876;

MAPLE

A360859 := (n, k) -> binomial(n, ceil(k/2)) * binomial(n, floor(k/2)):

seq(seq(A360859(n, k), k = 0..n), n = 0..10);

PROG

(Python)

from math import comb

def A360859_T(n, k): return comb(n, m:=k>>1)**2*(n-m)//(m+1) if k&1 else comb(n, k>>1)**2 # Chai Wah Wu, Feb 28 2023

CROSSREFS

Cf. A018224 (main diagonal), A360861 (row sums).

Cf. A360857, A360858.

Sequence in context: A275895 A369292 A158613 * A209573 A100075 A059836

Adjacent sequences: A360856 A360857 A360858 * A360860 A360861 A360862

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Feb 28 2023

STATUS

approved