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A014347 Three-fold exponential convolution of primes with themselves.

%I A014347 #15 Jun 05 2018 07:29:09
%S A014347 8,36,168,786,3660,16866,76752,343914,1514724,6543066,27699960,
%T A014347 114793386,466078116,1854554490,7248419496,27869755866,105687130980,
%U A014347 395978680266,1468425404328,5396913313866,19675676962308,71219609783946,256052236665192,914773982356902
%N A014347 Three-fold exponential convolution of primes with themselves.
%H A014347 Alois P. Heinz, <a href="/A014347/b014347.txt">Table of n, a(n) for n = 0..1000</a>
%F A014347 E.g.f.: (Sum_{k>=0} prime(k+1)*x^k/k!)^3. - _Ilya Gutkovskiy_, Mar 10 2018
%p A014347 b:= proc(n, k) option remember; `if`(k=1,
%p A014347       ithprime(n+1), add(b(j, floor(k/2))*
%p A014347       b(n-j, ceil(k/2))*binomial(n, j), j=0..n))
%p A014347     end:
%p A014347 a:= n-> b(n, 3):
%p A014347 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 10 2018
%t A014347 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 A014347 a[n_] := b[n, 3];
%t A014347 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jun 05 2018, after _Alois P. Heinz_ *)
%Y A014347 Cf. A000040, A014345, A014352.
%K A014347 nonn
%O A014347 0,1
%A A014347 _N. J. A. Sloane_