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

0,2

Links

Table of n, a(n) for n=0..13.

Formula

G.f.: sqrt( Sum_{n>=0} index of prime a(n+1) * x^n ).

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}]

Crossrefs

Cf. A000040, A000108, A014342, A007097, A093502, A338816.

Sequence in context: A255904 A046846 A111010 * A089307 A367902 A102896

Adjacent sequences: A363652 A363653 A363654 * A363656 A363657 A363658

Keyword

nonn,hard,more

Author

Ilya Gutkovskiy, Jun 13 2023

Extensions

a(12)-a(13) from Amiram Eldar, Jun 13 2023

Status

approved