A136104 A007318 * A002110; a(n) = Sum_{k=0..n} binomial(n,k)*A002110(k).

1, 3, 11, 55, 375, 3731, 47743, 777771, 14770535, 331611235, 9205305591, 285781156343, 10308779559631, 418386835375575, 18097509979840775, 846748292083023991, 44182142790019823943, 2570069981187508600331, 157428743473326543397855, 10449715795107936675445215, 739751959772798881608189731

Offset: 0

Author

Gary W. Adamson, Dec 14 2007

Keywords

• nonn

Examples

			a(3) = 55 = (1, 3, 3, 1) dot (1, 2, 6, 30) = (1 + 6 + 18 + 30), where A002110 = (1, 2, 6, 30, 210, 2310, ...).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..350
• Index entries for triangles and arrays related to Pascal's triangle
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A007188, A007318, A276085.

Leftmost column of A276586.

Cf. also A001339, A121572.

Programs

Maple

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):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 20 2016

Mathematica

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 *)

Formula

Binomial transform of primorial numbers, A002110.

a(n) = A276085(A007188(n)). - Antti Karttunen, Sep 18 2016

Extensions

A few more terms from L. Edson Jeffery, Apr 11 2011

Explicit binomial sum formula added to the name by Antti Karttunen, Sep 19 2016