JavaScript (Node.js), 120 bytes

n=6;a="2";for(;n-->0;a=a.split("").reverse().reduce((v,e,i)=>v.concat(Array(e*1).fill(i+1)),[]).join(""));console.log(a)

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Set n at the start to change which element of the sequence is calculated.

Unfortunately, this is a rather long answer, due to JavaScript's wordy array operator functions.

JavaScript (Node.js), 110 bytes

n=6;a=[2];for(;n-->0;a=a.reverse().reduce((v,e,i)=>v.concat(Array(e*1).fill(i+1)),[]));console.log(a.join(""))

Try it online!

Set n at the start to change which element of the sequence is calculated.

Unfortunately, this is a rather long answer, due to JavaScript's wordy array operator functions.

JavaScript (ES6), 139 bytes

n=6;a=[2];while(n-->0){a=a.join("").split("").reverse().reduce((v,e,i)=>v.concat(Array(parseInt(e)).fill(i+1)),[])};console.log(a.join(""))

Try it online!

Set n at the start to change which element of the sequence is calculated.

Unfortunately, this is a rather long answer, due to JavaScript's wordy array operator functions.

JavaScript (Node.js), 120 bytes

n=6;a="2";for(;n-->0;a=a.split("").reverse().reduce((v,e,i)=>v.concat(Array(e*1).fill(i+1)),[]).join(""));console.log(a)

Try it online!

Set n at the start to change which element of the sequence is calculated.

Unfortunately, this is a rather long answer, due to JavaScript's wordy array operator functions.

JavaScript (ES6), 144 bytes

n=6;a=[2];for(j=0;j<n;j++){a=a.join("").split("").reverse().reduce((v,e,i)=>v.concat(Array(parseInt(e)).fill(i+1)),[])};console.log(a.join(""));

JavaScript (ES6), 139 bytes

n=6;a=[2];while(n-->0){a=a.join("").split("").reverse().reduce((v,e,i)=>v.concat(Array(parseInt(e)).fill(i+1)),[])};console.log(a.join(""))

Try it online!

Set n at the start to change which element of the sequence is calculated.

Unfortunately, this is a rather long answer, due to JavaScript's wordy array operator functions.