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

0,2

Links

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

Formula

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

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

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 *)

Crossrefs

Cf. A000040, A309955, A340991.

Sequence in context: A140780 A268493 A002669 * A112711 A155651 A268020

Adjacent sequences: A340987 A340988 A340989 * A340991 A340992 A340993

Keyword

nonn

Author

Alois P. Heinz, Feb 01 2021

Status

approved