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A014352 Four-fold exponential convolution of primes with themselves.

%I A014352 #16 Jun 05 2018 07:31:45
%S A014352 16,96,592,3680,22888,141776,872296,5320160,32116168,191634736,
%T A014352 1128985544,6560592320,37577101096,212032652336,1178400630472,
%U A014352 6450745788064,34795044655624,185041871051312,971039709861320,5033044804735360,25793494764933224,130834363186542320
%N A014352 Four-fold exponential convolution of primes with themselves.
%H A014352 Alois P. Heinz, <a href="/A014352/b014352.txt">Table of n, a(n) for n = 0..1000</a>
%F A014352 E.g.f.: (Sum_{k>=0} prime(k+1)*x^k/k!)^4. - _Ilya Gutkovskiy_, Mar 10 2018
%p A014352 b:= proc(n, k) option remember; `if`(k=1,
%p A014352       ithprime(n+1), add(b(j, floor(k/2))*
%p A014352       b(n-j, ceil(k/2))*binomial(n, j), j=0..n))
%p A014352     end:
%p A014352 a:= n-> b(n, 4):
%p A014352 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 10 2018
%t A014352 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 A014352 a[n_] := b[n, 4];
%t A014352 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jun 05 2018, after _Alois P. Heinz_ *)
%Y A014352 Cf. A000040, A014345, A014347.
%K A014352 nonn
%O A014352 0,1
%A A014352 _N. J. A. Sloane_