OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's MathWorld, Reciprocal Multifactorial Constant
FORMULA
m(k) = (1/k)*exp(1/k)*(k + Sum_{j=1..k-1} (gamma(j/k) - gamma(j/k, 1/k)) where gamma(x) is the Euler gamma function and gamma(a,x) the incomplete gamma function.
EXAMPLE
3.9892412126901365441336421348019099438359273924576814826209556653...
MATHEMATICA
m[k_] := (1/k) Exp[1/k] (k + Sum[k^(j/k) (Gamma[j/k] - Gamma[j/k, 1/k]), {j, 1, k - 1}]); RealDigits[m[8], 10, 103][[1]]
PROG
(PARI) default(realprecision, 105); (1/8)*exp(1/8)*(8 + sum(k=1, 7, 8^(k/8)*(gamma(k/8) - incgam(k/8, 1/8)))) \\ G. C. Greubel, Mar 28 2019
(Magma) SetDefaultRealField(RealField(107)); (1/8)*Exp(1/8)*(8 + (&+[8^(k/8)*Gamma(k/8, 1/8): k in [1..7]])); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx((1/8)*exp(1/8)*(8 + sum(8^(k/8)*(gamma(k/8) - gamma_inc(k/8, 1/8)) for k in (1..7))), digits=105) # G. C. Greubel, Mar 28 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 05 2017
STATUS
approved