A333370 Convolution of primorial numbers (A002110) with themselves.

1, 4, 16, 84, 576, 5820, 72720, 1181460, 21984480, 493882620, 13996733520, 430612001820, 15742074348000, 641147559872820, 27488197348531920, 1286344285877911260, 67817877972050366160, 3984226025421591129180, 242703493548359285922480, 16211176424801583698573100

Offset: 0

Author

Ilya Gutkovskiy, Mar 17 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..350
• Eric Weisstein's World of Mathematics, Primorial
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A003149, A014342, A333371.

Programs

Maple

p:= proc(n) option remember; `if`(n<1, 1, ithprime(n)*p(n-1)) end:
a:= n-> add(p(i)*p(n-i), i=0..n):
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 17 2020

Mathematica

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}]

Formula

G.f.: (Sum_{k>=0} prime(k)# * x^k)^2, where prime()# = A002110.

a(n) = Sum_{k=0..n} prime(k)# * prime(n-k)#.