A131045 - OEIS

%I #11 Feb 26 2019 05:03:44

%S 1,2,5,12,29,68,155,348,775,1712,3745,8112,17431,37252,79355,168710,

%T 358037,758020,1599675,3362876,7041593,14692956,30577435,63531092,

%U 131901879,273804738,568366037,1179585610,2446603047,5068970880

%N Binomial transform of Euler's totient function phi(n+1).

%H Vaclav Kotesovec, <a href="/A131045/b131045.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum_{j=0..n} binomial(n,j)*phi(j+1). - _Emeric Deutsch_, Jul 09 2007

%e a(3) = (1,3,3,1) dot (1,1,2,2) = 1 + 3 + 6 + 2 = 12.

%p with(numtheory); a := proc (n) options operator, arrow; sum(binomial(n, j)*phi(j+1), j = 0 .. n) end proc; seq(a(n), n = 0 .. 30); # _Emeric Deutsch_, Jul 09 2007

%t Table[Sum[Binomial[n,k]*EulerPhi[k+1], {k, 0, n}], {n, 0, 30}] (* _Vaclav Kotesovec_, Oct 30 2017 *)

%o (PARI) a(n) = sum(j=0, n, binomial(n,j)*eulerphi(j+1)); \\ _Michel Marcus_, Feb 26 2019

%Y Cf. A000010, A007318.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Jun 11 2007

%E More terms from _Emeric Deutsch_, Jul 09 2007