A027873 a(n) = Product_{i=1..n} (6^i - 1).

1, 5, 175, 37625, 48724375, 378832015625, 17674407688984375, 4947685316415841015625, 8310206472731792807458984375, 83747726219216824716765369541015625

Offset

0,2

Links

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

Formula

5^n|a(n) for n>=0. - G. C. Greubel, Nov 20 2015

a(n) ~ c * 6^(n*(n+1)/2), where c = Product_{k>=1} (1-1/6^k) = A132034 = 0.805687728162164940923750215496298968917997628693... . - Vaclav Kotesovec, Nov 21 2015

a(n) = 6^(binomial(n+1,2))*(1/6;1/6)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. - G. C. Greubel, Dec 24 2015

a(n) = Product_{i=1..n} A024062(i). - Michel Marcus, Dec 27 2015

G.f.: Sum_{n>=0} 6^(n*(n+1)/2)*x^n / Product_{k=0..n} (1 + 6^k*x). - Ilya Gutkovskiy, May 22 2017

Sum_{n>=0} (-1)^n/a(n) = A132034. - Amiram Eldar, May 07 2023

Mathematica

Table[Product[(6^k-1), {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 17 2015 *)
Abs@QPochhammer[6, 6, Range[0, 10]] (* Vladimir Reshetnikov, Nov 20 2015 *)
FoldList[Times, Join[{1}, 6^Range[10]-1]] (* Harvey P. Dale, Oct 13 2017 *)

Prog

(PARI) a(n) = prod(i=1, n, 6^i-1); \\ Michel Marcus, Nov 21 2015
(Magma) [1] cat [&*[ 6^k-1: k in [1..n] ]: n in [1..11]]; // Vincenzo Librandi, Dec 24 2015

Crossrefs

Cf. A005329 (q=2), A027871 (q=3), A027637 (q=4), A027872 (q=5), A027875 (q=7), A027876 (q=8), A027877 (q=9), A027878 (q=10), A027879 (q=11), A027880 (q=12).

Cf. A132034.

Sequence in context: A303154 A060070 A300590 * A203529 A052272 A111515

Adjacent sequences: A027870 A027871 A027872 * A027874 A027875 A027876

Keyword

nonn

Author

N. J. A. Sloane

Status

approved