A027876 a(n) = Product_{i=1..n} (8^i - 1).

1, 7, 441, 225351, 922812345, 30237792108615, 7926625536728661945, 16623330670976050126618695, 278893192683059452825059069034425, 37432410397693271164043156886536608251975

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A005329 (q=2), A027871 (q=3), A027637 (q=4), A027872 (q=5), A027873 (q=6), A027875 (q=7), A027877 (q=9), A027878 (q=10), A027879 (q=11), A027880 (q=12).

Cf. A132036.

Programs

Magma

[1] cat [&*[ 8^k-1: k in [1..n] ]: n in [1..11]]; // Vincenzo Librandi, Dec 24 2015

Maple

seq(mul(8^i-1,i=1..n), n=0..20); # Robert Israel, Dec 24 2015

Mathematica

FoldList[Times,1,8^Range[10]-1] (* Harvey P. Dale, Dec 23 2011 *)

PARI

a(n)=prod(i=1,n,8^i-1) \\ Charles R Greathouse IV, Nov 22 2015

Formula

a(n) ~ c * 8^(n*(n+1)/2), where c = Product_{k>=1} (1-1/8^k) = A132036 = 0.859405994400702866200758580064418894909484979588... . - Vaclav Kotesovec, Nov 21 2015

7^n | a(n). - G. C. Greubel, Nov 21 2015

It appears that 7^m | a(n) iff 7^m | (7n)!. - Robert Israel, Dec 24 2015

a(n) = 8^(binomial(n+1,2))*(1/8;1/8){n}, where (a;q){n} is the q-Pochhammer symbol. - G. C. Greubel, Dec 24 2015

G.f. g(x) satisfies (1+x) g(x) = 1 + 8 x g(8x). - Robert Israel, Dec 24 2015

a(n) = Product_{i=1..n} A024088(i). - Michel Marcus, Dec 27 2015

G.f.: Sum_{n>=0} 8^(n*(n+1)/2)*x^n / Product_{k=0..n} (1 + 8^k*x). - Ilya Gutkovskiy, May 22 2017

Sum_{n>=0} (-1)^n/a(n) = A132036. - Amiram Eldar, May 07 2023