A370765 a(n) = 9^n * [x^n] Product_{k>=1} ((1 + 2^(k+1)*x^k) * (1 + 2^(k-1)*x^k))^(1/3).

1, 15, 153, 11295, 31968, 5289300, 41957514, 3216919050, -21009764691, 2153132775315, -16978376482767, 1659596014366335, -35929151338082922, 1473739361689662990, -38968782475183427016, 1541715187631618436300, -46858796372722560413526, 1615119529247884664988030

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

G.f.: Product_{k>=1} ((1 + 2^(k+1)*(9*x)^k) * (1 + 2^(k-1)*(9*x)^k))^(1/3).

a(n) ~ (-1)^(n+1) * c * 36^n / n^(4/3), where c = 0.244280405759762854740979712556383125782589356973734984...

Mathematica

nmax = 25; CoefficientList[Series[Product[(1+2^(k+1)*x^k)*(1+2^(k-1)*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]
nmax = 25; CoefficientList[Series[Product[(1+2^(k+1)*(9*x)^k)*(1+2^(k-1)*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]
nmax = 25; CoefficientList[Series[(2*QPochhammer[-2, 2*x]*QPochhammer[-1/2, 2*x]/9)^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]
nmax = 25; CoefficientList[Series[(2*QPochhammer[-2, x]*QPochhammer[-1/2, x]/9)^(1/3), {x, 0, nmax}], x] * 18^Range[0, nmax]

Crossrefs

Cf. A032302, A304961, A370016, A370761, A370764.

Sequence in context: A004322 A125403 A010035 * A334356 A017389 A278803

Adjacent sequences: A370762 A370763 A370764 * A370766 A370767 A370768

Keyword

sign

Author

Vaclav Kotesovec, Mar 01 2024

Status

approved