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

%I A014348 #13 Jul 08 2025 05:37:02
%S A014348 4,18,84,393,1830,8433,38376,171957,757362,3271533,13849980,57396693,
%T A014348 233039058,927277245,3624209748,13934877933,52843565490,197989340133,
%U A014348 734212702164,2698456656933,9837838481154,35609804891973,128026118332596,457386991178451
%N A014348 Three-fold exponential convolution of primes with themselves (divided by 2).
%H A014348 Alois P. Heinz, <a href="/A014348/b014348.txt">Table of n, a(n) for n = 0..1000</a>
%p A014348 b:= proc(n, k) option remember; `if`(k=1, ithprime(n+1), add(
%p A014348       b(j, floor(k/2))*b(n-j, ceil(k/2))*binomial(n, j), j=0..n))
%p A014348     end:
%p A014348 a:= n-> b(n, 3)/2:
%p A014348 seq(a(n), n=0..30);  # _Alois P. Heinz_, Jun 07 2018
%t A014348 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}]];
%t A014348 a[n_] := b[n, 3]/2;
%t A014348 a /@ Range[0, 30] (* _Jean-François Alcover_, Nov 16 2020, after _Alois P. Heinz_ *)
%Y A014348 Cf. A014347.
%K A014348 nonn
%O A014348 0,1
%A A014348 _N. J. A. Sloane_