A014347 Three-fold exponential convolution of primes with themselves.

8, 36, 168, 786, 3660, 16866, 76752, 343914, 1514724, 6543066, 27699960, 114793386, 466078116, 1854554490, 7248419496, 27869755866, 105687130980, 395978680266, 1468425404328, 5396913313866, 19675676962308, 71219609783946, 256052236665192, 914773982356902

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040, A014345, A014352.

Programs

Maple

b:= proc(n, k) option remember; `if`(k=1,
      ithprime(n+1), add(b(j, floor(k/2))*
      b(n-j, ceil(k/2))*binomial(n, j), j=0..n))
    end:
a:= n-> b(n, 3):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 10 2018

Mathematica

b[n_, k_] := b[n, k] = If[k == 1, Prime[n + 1], Sum[b[j, Floor[k/2]] b[n - j, Ceiling[k/2]] Binomial[n, j], {j, 0, n}]];
a[n_] := b[n, 3];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 05 2018, after Alois P. Heinz *)

Formula

E.g.f.: (Sum_{k>=0} prime(k+1)*x^k/k!)^3. - Ilya Gutkovskiy, Mar 10 2018