A014352 Four-fold exponential convolution of primes with themselves.

16, 96, 592, 3680, 22888, 141776, 872296, 5320160, 32116168, 191634736, 1128985544, 6560592320, 37577101096, 212032652336, 1178400630472, 6450745788064, 34795044655624, 185041871051312, 971039709861320, 5033044804735360, 25793494764933224, 130834363186542320

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, 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, 4):
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, 4];
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!)^4. - Ilya Gutkovskiy, Mar 10 2018