A363655 a(0) = 1; for n > 0, a(n) = prime( Sum_{k=0..n-1} a(k) * a(n-k-1) ).
1, 2, 7, 61, 863, 17569, 472741, 16007419, 659408567, 32231133931, 1833425773489, 119498316410171, 8810846732918257, 727089137774221667
Offset: 0
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = Prime[Sum[a[k] a[n - k - 1], {k, 0, n - 1}]]; Table[a[n], {n, 0, 11}]
Formula
G.f.: sqrt( Sum_{n>=0} index of prime a(n+1) * x^n ).
Extensions
a(12)-a(13) from Amiram Eldar, Jun 13 2023