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A014344 Four-fold convolution of primes with themselves.

%I A014344 #23 Feb 01 2021 19:00:05
%S A014344 16,96,376,1160,3121,7532,16754,34796,68339,127952,229956,398688,
%T A014344 669781,1094076,1742710,2713604,4139111,6195712,9115304,13199072,
%U A014344 18833449,26509260,36843322,50603884,68740107,92414192,123039628,162323200,212312453,275448380
%N A014344 Four-fold convolution of primes with themselves.
%H A014344 Alois P. Heinz, <a href="/A014344/b014344.txt">Table of n, a(n) for n = 0..1000</a>
%F A014344 G.f.: ((1/x)*Sum_{k>=1} prime(k)*x^k)^4. - _Ilya Gutkovskiy_, Mar 10 2018
%p A014344 b:= proc(n, k) option remember; `if`(k=1, ithprime(n+1),
%p A014344       add(b(j, floor(k/2))*b(n-j, ceil(k/2)), j=0..n))
%p A014344     end:
%p A014344 a:= n-> b(n, 4):
%p A014344 seq(a(n), n=0..35);  # _Alois P. Heinz_, Mar 10 2018
%t A014344 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}]];
%t A014344 a[n_] := b[n, 4];
%t A014344 a /@ Range[0, 35] (* _Jean-François Alcover_, Nov 16 2020, after _Alois P. Heinz_ *)
%o A014344 (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
%Y A014344 Cf. A000040, A014342, A014343.
%Y A014344 Column k=4 of A340991.
%K A014344 nonn
%O A014344 0,1
%A A014344 _N. J. A. Sloane_