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A333371
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Exponential convolution of primorial numbers (A002110) with themselves.
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2
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1, 4, 20, 132, 1116, 12420, 171300, 2884980, 56674380, 1289511300, 34769949060, 1063909626780, 37255008811020, 1470406699982220, 63114539746598340, 2936218980067393020, 150241360192861037100, 8497891914008911514100, 514514062115556069627060
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OFFSET
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0,2
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LINKS
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Eric Weisstein's World of Mathematics, Primorial
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FORMULA
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E.g.f.: (Sum_{k>=0} prime(k)# * x^k / k!)^2, where prime()# = A002110.
a(n) = Sum_{k=0..n} binomial(n,k) * prime(k)# * prime(n-k)#.
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MAPLE
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p:= proc(n) option remember; `if`(n<1, 1, ithprime(n)*p(n-1)) end:
a:= n-> add(p(i)*p(n-i)*binomial(n, i), i=0..n):
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MATHEMATICA
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primorial[n_] := Product[Prime[k], {k, 1, n}]; a[n_] := Sum[Binomial[n, k] primorial[k] primorial[n - k], {k, 0, n}]; Table[a[n], {n, 0, 18}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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