A251662 Dirichlet convolution of Moebius function mu(n) (A008683) with Ternary numbers A001764.

1, 0, 2, 11, 54, 270, 1427, 7740, 43260, 246620, 1430714, 8414356, 50067107, 300829144, 1822766463, 11124747912, 68328754958, 422030501802, 2619631042664, 16332922043614, 102240109896265, 642312449787030, 4048514844039119, 25594403732709300, 162250238001816845, 1031147983109715120

Offset

1,3

Links

Table of n, a(n) for n=1..26.

Formula

G.f. A(x) satisfies: Sum_{n>=1} A((x - 2*x^2 + x^3)^n) = x - x^2.

a(n) = Sum_{d|n} Moebius(n/d) * binomial(3*(d-1), d-1)/(2*d-1).

Example

G.f.: A(x) = x + 2*x^3 + 11*x^4 + 54*x^5 + 270*x^6 + 1427*x^7 + 7740*x^8 +...
where Sum_{n>=1} A(x^n*(1-x)^(2*n)) = x - x^2:
x-x^2 = A(x*(1-x)^2) + A(x^2*(1-x)^4) + A(x^3*(1-x)^6) + A(x^4*(1-x)^8) +...

Prog

(PARI) /* Dirichlet convolution of mu(n) with Ternary numbers A001764: */
{a(n) = sumdiv(n, d, moebius(n/d) * binomial(3*(d-1), d-1)/(2*d-1))}
for(n=1, 30, print1(a(n), ", "))
(PARI) /* G.f. satisfies: Sum_{n>=1} A(x^n*(1-x)^(2*n)) = x-x^2. */
{a(n)=local(A=[1, 0]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(sum(n=1, #A, subst(x*Ser(A), x, (x-2*x^2+x^3 +x*O(x^#A))^n)))[#A]); A[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A034742, A001764, A008683.

Sequence in context: A161559 A291386 A128748 * A327215 A307444 A037522

Adjacent sequences: A251659 A251660 A251661 * A251663 A251664 A251665

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2015

Status

approved