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

1,1

Links

Table of n, a(n) for n=1..23.

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.

Mathematica

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

Prog

(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), ", "))

Crossrefs

Cf. A008683, A212442, A203853, A002203.

Sequence in context: A071357 A142872 A113995 * A294036 A097679 A158778

Adjacent sequences: A212440 A212441 A212442 * A212444 A212445 A212446

Keyword

nonn

Author

Paul D. Hanna, May 17 2012

Status

approved