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

0-indexed.

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    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")