A375959 Partial products of A006257.

1, 1, 3, 3, 9, 45, 315, 315, 945, 4725, 33075, 297675, 3274425, 42567525, 638512875, 638512875, 1915538625, 9577693125, 67043851875, 603394666875, 6637341335625, 86285437363125, 1294281560446875, 22002786527596875, 418052944024340625, 8779111824511153125, 201919571963756521875

Offset: 1

Author

Darío Clavijo, Sep 03 2024

Keywords

• nonn
• easy

Comments

Also the determinant of the n X n lower triangular matrix where row j is the Eytzinger array permutation of {1,2,...,j} (A375825), and similarly any lower triangular matrices with A006257 on their diagonal.

a(n) = a(n-1) iff n = 2^k, since those n are where A006257(n) = 1. - Stefano Spezia, Sep 06 2024

Examples

			For n = 9, a(9) = 1*1*3*1*3*5*7*1*3 = 945.
		

Links

• Sergey Slotin, Eytzinger binary search.

Crossrefs

Cf. A006257, A375825.

Programs

Mathematica

Table[Product[Flatten[Table[Range[1, 2^n - 1, 2], {n, 1, 6}]][[i]],{i,n}],{n,1,27}] (* James C. McMahon, Sep 19 2024 *)

PARI

a(n) = prod(k=1, n, 2*k-2^logint(2*k, 2)+1); \\ Michel Marcus, Sep 06 2024

Python

from sympy import prod
a = lambda n: prod(((j-(1 << j.bit_length()-1))<<1)+1 for j in range(1, n+1))
print([a(n) for n in range(1, 28)])

Formula

a(n) = Product_{k=1..n} A006257(k).