A269353 Expansion of 1/(1-2x/(1-3x/(1-5x/(1-7x/(1-11x/...))))) where 2,3,5,7,11,... are the prime numbers.

1, 2, 10, 80, 910, 14180, 294820, 7898900, 262166950, 10401023300, 480352145980, 25403319156500, 1524514142067820, 103259722304891000, 7855753426977689320, 667222680003329539400, 62774912079259300426030, 6482982674137778455277720, 728040412975153836997647580

Offset: 0

Author

Benedict W. J. Irwin, Feb 25 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000040, A285407.

Programs

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]

Formula

G.f.: 1/(1-2x/(1-3x/(1-5x/(1-7x/(1-11x/(1-13x/(...))))))), by definition.

Extensions

Offset corrected by Vaclav Kotesovec, Aug 26 2017