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A370734
a(n) = 8^n * [x^n] Product_{k>=1} 1/(1 - 3*x^k)^(1/4).
1
1, 6, 138, 2292, 47046, 852756, 18266628, 366635112, 7948637382, 170568754692, 3761729402412, 83136335360856, 1863229219846428, 41883396293989320, 948524060727094728, 21555960625992644304, 492036151405623971142, 11264431786398948383844, 258676355450246122857756
OFFSET
0,2
FORMULA
G.f.: Product_{k>=1} 1/(1 - 3*(8*x)^k)^(1/4).
a(n) ~ 24^n / (Gamma(1/4) * QPochhammer(1/3)^(1/4) * n^(3/4)).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1-3*x^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x] * 8^Range[0, nmax]
nmax = 20; CoefficientList[Series[Product[1/(1-3*(8*x)^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x]
CROSSREFS
Cf. A242587 (m=1), A370714 (m=2), A370710 (m=3), A370735 (m=5).
Sequence in context: A075185 A376113 A003994 * A307353 A366227 A155558
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 28 2024
STATUS
approved