A212443 a(n) = (1/n) * Sum_{d|n} moebius(n/d) * A002203(d)^2, where A002203 is the companion Pell numbers.

4, 16, 64, 280, 1344, 6496, 32640, 166320, 862400, 4523232, 23970240, 128063040, 689008320, 3728973120, 20285199872, 110841302880, 608029121280, 3346972244000, 18480871268160, 102328688556864, 568014587806720, 3160148362953120, 17617881702072960

Offset: 1

Author

Paul D. Hanna, May 17 2012

Keywords

• nonn

Crossrefs

Cf. A008683, A212442, A203853, A002203.

Programs

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#] * LucasL[#, 2]^2 &] / n; Array[a, 25] (* Amiram Eldar, Aug 22 2023 *)

PARI

{A002203(n)=polcoeff(2*x*(1+x)/(1-2*x-x^2+x*O(x^n)),n)}
{a(n)=if(n<1, 0, sumdiv(n, d, moebius(n/d)*A002203(d)^2)/n)}
for(n=1,30,print1(a(n),","))

Formula

G.f.: 1/Product_{n>=1} (1 - A002203(n)*x^n + (-1)^n*x^(2*n))^a(n) = exp(Sum_{n>=1} A002203(n)^3 * x^n/n), which equals the g.f. of A212442.