A269694 - OEIS

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A269694

Product of first n nonzero Jacobsthal numbers (A001045).

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

(list; graph; refs; listen; history; text; internal format)

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.