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A370737 a(n) = 5^(2*n) * [x^n] Product_{k>=1} (1 + 2*x^k)^(1/5). 2
1, 10, 50, 14750, -166250, 14011250, -133418750, 18136968750, -620089531250, 29520532031250, -917207280468750, 51260806902343750, -2257145499863281250, 101035630688769531250, -4434459153208496093750, 214279556679692871093750, -9859289197933918457031250, 454976266920750451660156250 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{k>=1} (1 + 2*(25*x)^k)^(1/5).
a(n) ~ (-1)^(n+1) * QPochhammer(-1/2)^(1/5) * 50^n / (5 * Gamma(4/5) * n^(6/5)).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1+2*x^k, {k, 1, nmax}]^(1/5), {x, 0, nmax}], x] * 25^Range[0, nmax]
nmax = 20; CoefficientList[Series[Product[1+2*(25*x)^k, {k, 1, nmax}]^(1/5), {x, 0, nmax}], x]
CROSSREFS
Cf. A032302 (m=1), A370709 (m=2), A370716 (m=3), A370736 (m=4).
Sequence in context: A072296 A143558 A106041 * A264044 A143855 A124162
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Feb 28 2024
STATUS
approved

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Last modified July 12 14:24 EDT 2024. Contains 374251 sequences. (Running on oeis4.)