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A370714 a(n) = 4^n * [x^n] Product_{k>=1} 1/(1 - 3*x^k)^(1/2). 4
1, 6, 78, 780, 8790, 90708, 1015692, 10964760, 122893926, 1370476932, 15518261220, 176063641512, 2014426860540, 23109736996680, 266397931733208, 3079014279154224, 35695144493030022, 414708043501061988, 4828444403991450612, 56314242827277224712, 657855733949279381652 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{k>=1} 1/(1 - 3*(4*x)^k)^(1/2).
a(n) ~ 12^n / sqrt(Pi*QPochhammer(1/3)*n).
MATHEMATICA
nmax = 25; CoefficientList[Series[Product[1/(1-3*x^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x] * 4^Range[0, nmax]
nmax = 25; CoefficientList[Series[Product[1/(1-3*(4*x)^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x]
nmax = 25; CoefficientList[Series[Sqrt[-2/QPochhammer[3, x]], {x, 0, nmax}], x] * 4^Range[0, nmax]
CROSSREFS
Sequence in context: A069669 A145359 A306096 * A145360 A183405 A068884
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 27 2024
STATUS
approved

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Last modified July 19 03:15 EDT 2024. Contains 374388 sequences. (Running on oeis4.)