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A375959
Partial products of A006257.
0
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
1,3
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
FORMULA
a(n) = Product_{k=1..n} A006257(k).
EXAMPLE
For n = 9, a(9) = 1*1*3*1*3*5*7*1*3 = 945.
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 *)
PROG
(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)])
(PARI) a(n) = prod(k=1, n, 2*k-2^logint(2*k, 2)+1); \\ Michel Marcus, Sep 06 2024
CROSSREFS
Sequence in context: A038080 A257621 A190960 * A257623 A257625 A216147
KEYWORD
nonn,easy
AUTHOR
Darío Clavijo, Sep 03 2024
STATUS
approved