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

%I A136104 #29 Mar 27 2022 23:29:52
%S A136104 1,3,11,55,375,3731,47743,777771,14770535,331611235,9205305591,
%T A136104 285781156343,10308779559631,418386835375575,18097509979840775,
%U A136104 846748292083023991,44182142790019823943,2570069981187508600331,157428743473326543397855,10449715795107936675445215,739751959772798881608189731
%N A136104 A007318 * A002110; a(n) = Sum_{k=0..n} binomial(n,k)*A002110(k).
%H A136104 Alois P. Heinz, <a href="/A136104/b136104.txt">Table of n, a(n) for n = 0..350</a>
%H A136104 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%H A136104 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A136104 Binomial transform of primorial numbers, A002110.
%F A136104 a(n) = A276085(A007188(n)). - _Antti Karttunen_, Sep 18 2016
%e A136104 a(3) = 55 = (1, 3, 3, 1) dot (1, 2, 6, 30) = (1 + 6 + 18 + 30), where A002110 = (1, 2, 6, 30, 210, 2310, ...).
%p A136104 b:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*b(n-1)) end:
%p A136104 a:= n-> add(binomial(n, k)*b(k), k=0..n):
%p A136104 seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 20 2016
%t A136104 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 *)
%Y A136104 Cf. A002110, A007188, A007318, A276085.
%Y A136104 Leftmost column of A276586.
%Y A136104 Cf. also A001339, A121572.
%K A136104 nonn
%O A136104 0,2
%A A136104 _Gary W. Adamson_, Dec 14 2007
%E A136104 A few more terms from _L. Edson Jeffery_, Apr 11 2011
%E A136104 Explicit binomial sum formula added to the name by _Antti Karttunen_, Sep 19 2016