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A269353
Expansion of 1/(1-2x/(1-3x/(1-5x/(1-7x/(1-11x/...))))) where 2,3,5,7,11,... are the prime numbers.
4
1, 2, 10, 80, 910, 14180, 294820, 7898900, 262166950, 10401023300, 480352145980, 25403319156500, 1524514142067820, 103259722304891000, 7855753426977689320, 667222680003329539400, 62774912079259300426030, 6482982674137778455277720, 728040412975153836997647580
OFFSET
0,2
LINKS
FORMULA
G.f.: 1/(1-2x/(1-3x/(1-5x/(1-7x/(1-11x/(1-13x/(...))))))), by definition.
MAPLE
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):
seq(a(n), n=0..20); # Alois P. Heinz, Nov 12 2023
MATHEMATICA
CoefficientList[Series[1/(1+ContinuedFractionK[-Prime[k]*x, 1, {k, 1, 50}]), {x, 0, 50}], x]
CROSSREFS
Sequence in context: A008544 A133480 A227464 * A064312 A063902 A088351
KEYWORD
nonn
AUTHOR
EXTENSIONS
Offset corrected by Vaclav Kotesovec, Aug 26 2017
STATUS
approved