A340990 a(n) is the (2n)-th term of the n-fold self-convolution of the primes.

1, 3, 29, 291, 3121, 34123, 379853, 4280251, 48681569, 557686227, 6425630909, 74384480019, 864461820049, 10079577033243, 117859582680813, 1381492094548651, 16227770995740865, 190979248798795427, 2251327736286726749, 26579050506578504195, 314212180691846338801

Offset: 0

Author

Alois P. Heinz, Feb 01 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..924

Crossrefs

Cf. A000040, A309955, A340991.

Programs

Maple

b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, ithprime(n+1),
      (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..23);

Mathematica

b[n_, k_] := b[n, k] = If[k == 0, 1, If[k == 1, Prime[n + 1], With[{q = Quotient[k, 2]}, Sum[b[j, q] b[n - j, k - q], {j, 0, n}]]]];
a[n_] := b[n, n];
a /@ Range[0, 23] (* Jean-François Alcover, Feb 04 2021, after Alois P. Heinz *)

Formula

a(n) = [x^(2n)] (Sum_{j>=1} prime(j)*x^j)^n.

a(n) = A340991(2n,n).