A027879 a(n) = Product_{i=1..n} (11^i - 1).

1, 10, 1200, 1596000, 23365440000, 3763004112000000, 6666387564654720000000, 129909027758312519942400000000, 27847153692160782464830528512000000000, 65662131721505488121539650946349537280000000000

Offset

0,2

Comments

It appears that the number of trailing zeros in a(n) is A191610(n). - Robert Israel, Nov 24 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..43

Formula

10^n|a(n) for n>=0; 12*(10)^(n)|a(n) n>=2. - G. C. Greubel, Nov 21 2015

a(n) ~ c * 11^(n*(n+1)/2), where c = Product_{k>=1} (1-1/11^k) = 0.900832706809715279949862694760647744762491192216... . - Vaclav Kotesovec, Nov 21 2015

E.g.f. E(x) satisfies E'(x) = 11 E(11 x) - E(x). - Robert Israel, Nov 24 2015

Equals 11^(binomial(n+1,2))*(1/11;1/11)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. - G. C. Greubel, Dec 24 2015

G.f.: Sum_{n>=0} 11^(n*(n+1)/2)*x^n / Product_{k=0..n} (1 + 11^k*x). - Ilya Gutkovskiy, May 22 2017

Sum_{n>=0} (-1)^n/a(n) = A132267. - Amiram Eldar, May 07 2023

Maple

seq(mul(11^i-1, i=1..n), n=0..20; # Robert Israel, Nov 24 2015

Mathematica

FoldList[Times, 1, 11^Range[10]-1] (* Harvey P. Dale, Aug 13 2013 *)
Abs@QPochhammer[11, 11, Range[0, 40]] (* G. C. Greubel, Nov 24 2015 *)

Prog

(PARI) a(n)=prod(i=1, n, 11^i-1) \\ Anders Hellström, Nov 21 2015
(Magma) [1] cat [&*[11^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), A027873 (q=6), A027875 (q=7), A027876 (q=8), A027877 (q=9), A027878 (q=10), A027880 (q=12).

Cf. A132267, A191610.

Sequence in context: A223119 A233252 A249849 * A194497 A287226 A015108

Adjacent sequences: A027876 A027877 A027878 * A027880 A027881 A027882

Keyword

nonn

Author

N. J. A. Sloane

Status

approved