#JavaScript (ES6), 42 bytes

A port of [xnor's solution][1].

0-indexed.

<!-- language-all: lang-javascript -->

    f=(n,k=2)=>n<3||k<n&&f(k)*f(n+~++k)+f(n,k)

[Try it online!](https://tio.run/##FctBDoIwEEDRPaeYBSEzDhqDS1rOQoPUaMkMAeOm1KtXu/qb91/u4/Zpe67vs@h9ztlblDbYjuwg5nYcwUjTeAx08ij8ZQ7EvhDKXjcUsHDtQcBAV8pMECuASWXXZb4s@sDRYR0l0Z/WscyURuqrlH8 "JavaScript (Node.js) – Try It Online")

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#JavaScript (ES6), <s>&nbsp;83&nbsp;</s> 75 bytes

A faster, less recursive, but significantly longer solution.

0-indexed.

<!-- language-all: lang-javascript -->

    f=(n,i,a=[p=1])=>a[n]||f(n,-~i,[...a,p+=(h=k=>k<i&&a[k]*a[i-++k]+h(k))(2)])

[Try it online!](https://tio.run/##FY1BCoMwEADvfcUeRLJNDK1XXT8SAi5WaxpJREsvar@e2tPAMDAv/vDaLW5@FyE@@pQGEkE5xWRmulukhk2w@z6ctvg6ZbTWrGZJYiRPja9dnrPx9srGFVJ6K0fhEUWJFtMQFxGA4FZBgBrKP6VE2C4AXQxrnHo9xadoWWRbOPBMs@084dFidTnSDw "JavaScript (Node.js) – Try It Online")


  [1]: https://codegolf.stackexchange.com/a/193186/58563