A131045 Binomial transform of Euler's totient function phi(n+1).
1, 2, 5, 12, 29, 68, 155, 348, 775, 1712, 3745, 8112, 17431, 37252, 79355, 168710, 358037, 758020, 1599675, 3362876, 7041593, 14692956, 30577435, 63531092, 131901879, 273804738, 568366037, 1179585610, 2446603047, 5068970880
Offset: 0
Keywords
Examples
a(3) = (1,3,3,1) dot (1,1,2,2) = 1 + 3 + 6 + 2 = 12.
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
Programs
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Maple
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
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Mathematica
Table[Sum[Binomial[n,k]*EulerPhi[k+1], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 30 2017 *) -
PARI
a(n) = sum(j=0, n, binomial(n,j)*eulerphi(j+1)); \\ Michel Marcus, Feb 26 2019
Formula
a(n) = Sum_{j=0..n} binomial(n,j)*phi(j+1). - Emeric Deutsch, Jul 09 2007
Extensions
More terms from Emeric Deutsch, Jul 09 2007