A014344 Four-fold convolution of primes with themselves.

16, 96, 376, 1160, 3121, 7532, 16754, 34796, 68339, 127952, 229956, 398688, 669781, 1094076, 1742710, 2713604, 4139111, 6195712, 9115304, 13199072, 18833449, 26509260, 36843322, 50603884, 68740107, 92414192, 123039628, 162323200, 212312453, 275448380

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, A014342, A014343.

Column k=4 of A340991.

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)), j=0..n))
    end:
a:= n-> b(n, 4):
seq(a(n), n=0..35);  # 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]], {j, 0, n}]];
a[n_] := b[n, 4];
a /@ Range[0, 35] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

PARI

my(N = 50, x = 'x + O('x^N)); Vec(((1/x)*sum(k=1, N, prime(k)*x^k))^4) \\ Michel Marcus, Mar 10 2018

Formula

G.f.: ((1/x)*Sum_{k>=1} prime(k)*x^k)^4. - Ilya Gutkovskiy, Mar 10 2018