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A322505
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Factorial expansion of 1/sqrt(2) = Sum_{n>=1} a(n)/n!.
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0
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0, 1, 1, 0, 4, 5, 0, 6, 4, 9, 0, 11, 7, 3, 11, 10, 2, 2, 5, 16, 11, 3, 7, 18, 16, 19, 11, 12, 21, 19, 22, 5, 31, 21, 25, 30, 20, 6, 5, 21, 17, 41, 36, 14, 28, 13, 45, 16, 0, 33, 1, 2, 41, 1, 28, 43, 9, 15, 16, 28, 22, 19, 22, 13, 34, 61, 38, 40, 56, 44, 69, 25, 42, 44, 34, 73, 71, 42, 17
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OFFSET
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1,5
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LINKS
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EXAMPLE
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1/sqrt(2) = 0 + 1/2! + 1/3! + 0/4! + 4/5! + 5/6! + 0/7! + 6/8! + ...
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MATHEMATICA
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With[{b = 1/Sqrt[2]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Dec 12 2018 *)
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PROG
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(PARI) default(realprecision, 250); b = 1/sqrt(2); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))
(Magma) SetDefaultRealField(RealField(250)); [Floor(1/Sqrt(2))] cat [Floor(Factorial(n)/Sqrt(2)) - n*Floor(Factorial((n-1))/Sqrt(2)) : n in [2..80]];
(Sage)
b=1/sqrt(2);
def a(n):
if (n==1): return floor(b)
else: return expand(floor(factorial(n)*b) -n*floor(factorial(n-1)*b))
[a(n) for n in (1..80)]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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