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A269353
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Expansion of 1/(1-2x/(1-3x/(1-5x/(1-7x/(1-11x/...))))) where 2,3,5,7,11,... are the prime numbers.
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4
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1, 2, 10, 80, 910, 14180, 294820, 7898900, 262166950, 10401023300, 480352145980, 25403319156500, 1524514142067820, 103259722304891000, 7855753426977689320, 667222680003329539400, 62774912079259300426030, 6482982674137778455277720, 728040412975153836997647580
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 1/(1-2x/(1-3x/(1-5x/(1-7x/(1-11x/(1-13x/(...))))))), by definition.
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MAPLE
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b:= proc(x, y) option remember; `if`(x=0 and y=0, 1,
`if`(x>0, b(x-1, y)*ithprime(y-x+1), 0)+`if`(y>x, b(x, y-1), 0))
end:
a:= n-> b(n$2):
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MATHEMATICA
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CoefficientList[Series[1/(1+ContinuedFractionK[-Prime[k]*x, 1, {k, 1, 50}]), {x, 0, 50}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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