A269694 Product of first n nonzero Jacobsthal numbers (A001045).

1, 1, 3, 15, 165, 3465, 148995, 12664575, 2165642325, 738484032825, 504384594419475, 688484971382583375, 1880252456845835197125, 10268058666835106011499625, 112158004817839862963610403875

Offset

1,3

Comments

Inspired by A015013.

Links

Table of n, a(n) for n=1..15.

Formula

a(n) = abs(A015013(n)).

a(n) ~ c * 2^(n*(n+1)/2) / 3^n, where c = QPochhammer(-2, 1/4)*QPochhammer(1/4)/3 = 1.21072413030105918013617285610590504636804163112313764347615924554000... - Vaclav Kotesovec, Mar 04 2021, updated Jul 19 2021

Equivalently, c = QPochhammer(-1/2). - Vaclav Kotesovec, Sep 24 2023

Example

a(4) = 15 because a(4) = 1*1*3*5 = 15.

Mathematica

Table[Abs@QFactorial[n, -2], {n, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)
FoldList[Times, LinearRecurrence[{1, 2}, {1, 1}, 20]] (* Harvey P. Dale, Apr 22 2019 *)
Table[(-1)^Floor[n/2] * QPochhammer[-2, 4, 1 + Floor[(n-1)/2]] * QPochhammer[4, 4, Floor[n/2]]/3^n, {n, 1, 20}] (* Vaclav Kotesovec, Mar 04 2021 *)

Prog

(PARI) a001045(n) = (2^n - (-1)^n) / 3;
a(n) = prod(i=1, n, a001045(i));

Crossrefs

Cf. A001045, A015013.

Sequence in context: A097489 A080696 A015013 * A153280 A132683 A059386

Adjacent sequences: A269691 A269692 A269693 * A269695 A269696 A269697

Keyword

nonn,easy

Author

Altug Alkan, Apr 05 2016

Status

approved