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A333370 Convolution of primorial numbers (A002110) with themselves.

%I A333370 #10 Feb 16 2025 08:33:59
%S A333370 1,4,16,84,576,5820,72720,1181460,21984480,493882620,13996733520,
%T A333370 430612001820,15742074348000,641147559872820,27488197348531920,
%U A333370 1286344285877911260,67817877972050366160,3984226025421591129180,242703493548359285922480,16211176424801583698573100
%N A333370 Convolution of primorial numbers (A002110) with themselves.
%H A333370 Alois P. Heinz, <a href="/A333370/b333370.txt">Table of n, a(n) for n = 0..350</a>
%H A333370 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Primorial.html">Primorial</a>
%H A333370 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A333370 G.f.: (Sum_{k>=0} prime(k)# * x^k)^2, where prime()# = A002110.
%F A333370 a(n) = Sum_{k=0..n} prime(k)# * prime(n-k)#.
%p A333370 p:= proc(n) option remember; `if`(n<1, 1, ithprime(n)*p(n-1)) end:
%p A333370 a:= n-> add(p(i)*p(n-i), i=0..n):
%p A333370 seq(a(n), n=0..20);  # _Alois P. Heinz_, Mar 17 2020
%t A333370 primorial[n_] := Product[Prime[k], {k, 1, n}]; a[n_] := Sum[primorial[k] primorial[n - k], {k, 0, n}]; Table[a[n], {n, 0, 19}]
%Y A333370 Cf. A002110, A003149, A014342, A333371.
%K A333370 nonn
%O A333370 0,2
%A A333370 _Ilya Gutkovskiy_, Mar 17 2020