OFFSET
1,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Harmonic Expansion
FORMULA
Sum_{n>=1} a(n)/n! = Euler gamma = A001620. - G. C. Greubel, Nov 26 2018
EXAMPLE
Euler gamma = 0 + 1/2! + 0/3! + 1/4! + 4/5! + 1/6! + 4/7! + 1/8! + ...
MATHEMATICA
With[{b = EulerGamma}, Table[If[n==1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Nov 26 2018 *)
PROG
(PARI) default(realprecision, 250); b = Euler; for(n=1, 80, print1( if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ G. C. Greubel, Nov 26 2018
(Magma) SetDefaultRealField(RealField(250)); [Floor(EulerGamma(250))] cat [Floor(Factorial(n)*EulerGamma(250)) - n*Floor(Factorial((n-1))*EulerGamma(250)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018
(Sage)
b = euler_gamma;
def A096622(n):
if (n==1): return floor(b)
else: return expand(floor(factorial(n)*b) -n*floor(factorial(n-1)*b))
[A096622(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 01 2004
STATUS
approved