A372870 G.f. A(x) satisfies A(x)^3 = A(x^3) / (1 - 3*x)^3 with A(0)=1.

1, 3, 9, 28, 84, 252, 758, 2274, 6822, 20471, 61413, 184239, 552729, 1658187, 4974561, 14923714, 44771142, 134313426, 402940361, 1208821083, 3626463249, 10879389971, 32638169913, 97914509739, 293743529832, 881230589496, 2643691768488, 7931075307172

Offset

0,2

Comments

Euler transform of 3 * A046211(n).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

OEIS Wiki, Euler transform

Formula

G.f.: A(x) = 1 / ( Product_{k>=1} (1 - x^k)^A046211(k) )^3.

Example

A(x)^3 = 1 + 9*x + 54*x^2 + 273*x^3 + 1242*x^4 + 5265*x^5 + 21231*x^6 + ... .

Prog

(PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
my(N=30, x='x+O('x^N)); Vec(1/prod(k=1, N, (1 - x^k)^b(k, 3))^3)

Crossrefs

Cf. A372956, A372957.

Cf. A046211, A271929.

Sequence in context: A292328 A027090 A033139 * A291731 A291257 A005354

Adjacent sequences: A372867 A372868 A372869 * A372871 A372872 A372873

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2024

Status

approved