A372957 G.f. A(x) satisfies A(x)^2 = A(x^2) / (1 - 2*x)^2 with A(0)=1.

1, 2, 5, 10, 22, 44, 91, 182, 370, 740, 1490, 2980, 5979, 11958, 23950, 47900, 95865, 191730, 383580, 767160, 1534549, 3069098, 6138628, 12277256, 24555341, 49110682, 98222947, 196445894, 392894839, 785789678, 1571585230, 3143170460, 6286352290, 12572704580, 25145431172

Offset

0,2

Comments

Euler transform of 2 * A000048(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)^A000048(k) )^2.

Example

A(x)^2 = 1 + 4*x + 14*x^2 + 40*x^3 + 109*x^4 + 276*x^5 + 678*x^6 + ... .

Prog

(PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
my(N=40, x='x+O('x^N)); Vec(1/prod(k=1, N, (1 - x^k)^b(k, 2))^2)

Crossrefs

Cf. A372870, A372956.

Cf. A000048, A123916.

Sequence in context: A215422 A026633 A093370 * A094537 A135098 A136488

Adjacent sequences: A372954 A372955 A372956 * A372958 A372959 A372960

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2024

Status

approved