A014348 Three-fold exponential convolution of primes with themselves (divided by 2).

4, 18, 84, 393, 1830, 8433, 38376, 171957, 757362, 3271533, 13849980, 57396693, 233039058, 927277245, 3624209748, 13934877933, 52843565490, 197989340133, 734212702164, 2698456656933, 9837838481154, 35609804891973, 128026118332596, 457386991178451

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Cf. A014347.

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)/2:
seq(a(n), n=0..30);  # Alois P. Heinz, Jun 07 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]/2;
a /@ Range[0, 30] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)