A081875 a(n) = Sum_{d|n} phi(n/d)*C(2*d,d)/2.

1, 4, 12, 40, 130, 480, 1722, 6480, 24336, 92520, 352726, 1352640, 5200312, 20060040, 77559060, 300546720, 1166803126, 4537592928, 17672631918, 68923357200, 269128940724, 1052049834616, 4116715363822, 16123803207552

Offset

1,2

Links

Table of n, a(n) for n=1..24.

V. A. Liskovets, Enumerative formulas for unrooted planar maps: a pattern, Electron. J. Combin., 11:1 (2004), R88.

J. Malenfant, On the Matrix-Element Expansion of a Circulant Determinant, arXiv preprint arXiv:1502.06012 [math.NT], 2015.

Formula

Dirichlet convolution of A000010 and A088218. - R. J. Mathar, Mar 11 2017

a(n) ~ 2^(2*n-1) / sqrt(Pi*n). - Vaclav Kotesovec, Jun 08 2019

From Richard L. Ollerton, May 07 2021: (Start)

a(n) = Sum_{k=1..n} C(2*gcd(n,k),gcd(n,k))/2.

a(n) = Sum_{k=1..n} A088218(gcd(n,k)). (End)

Example

G.f. = x + 4*x^2 + 12*x^3 + 40*x^4 + 130*x^5 + 480*x^6 + 1722*x^7 + ...

Mathematica

Table[Fold[ #1+EulerPhi[n/#2]*Binomial[2#2, #2]/2&, 0, Divisors[n]], {n, 1, 32}]
a[ n_] := If[ n < 0, 0, Sum[ Binomial[2 d, d] EulerPhi[n / d], {d, Divisors @ n}] / 2]; (* Michael Somos, Nov 01 2014 *)

Prog

(PARI) {a(n) = if( n<1, 0, sumdiv(n, d, binomial(2*d, d) * eulerphi(n/d)) / 2)}; /* Michael Somos, Nov 01 2014 */

Crossrefs

Cf. A045630.

Sequence in context: A087206 A275863 A289653 * A102433 A221652 A259806

Adjacent sequences: A081872 A081873 A081874 * A081876 A081877 A081878

Keyword

easy,nonn

Author

Wouter Meeussen, Apr 12 2003

Status

approved