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1, 3, 11, 55, 375, 3731, 47743, 777771, 14770535, 331611235, 9205305591, 285781156343, 10308779559631, 418386835375575, 18097509979840775, 846748292083023991, 44182142790019823943, 2570069981187508600331, 157428743473326543397855, 10449715795107936675445215, 739751959772798881608189731
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OFFSET
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0,2
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LINKS
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FORMULA
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Binomial transform of primorial numbers, A002110.
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EXAMPLE
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a(3) = 55 = (1, 3, 3, 1) dot (1, 2, 6, 30) = (1 + 6 + 18 + 30), where A002110 = (1, 2, 6, 30, 210, 2310, ...).
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*b(n-1)) end:
a:= n-> add(binomial(n, k)*b(k), k=0..n):
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MATHEMATICA
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b[n_] := b[n] = If[n==0, 1, Prime[n]*b[n-1]]; a[n_] := Sum[Binomial[n, k]*b[k], {k, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 22 2017, translated from Maple *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Explicit binomial sum formula added to the name by Antti Karttunen, Sep 19 2016
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STATUS
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approved
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