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A288095
Decimal expansion of m(8) = Sum_{n>=0} 1/n!8, the 8th reciprocal multifactorial constant.
10
3, 9, 8, 9, 2, 4, 1, 2, 1, 2, 6, 9, 0, 1, 3, 6, 5, 4, 4, 1, 3, 3, 6, 4, 2, 1, 3, 4, 8, 0, 1, 9, 0, 9, 9, 4, 3, 8, 3, 5, 9, 2, 7, 3, 9, 2, 4, 5, 7, 6, 8, 1, 4, 8, 2, 6, 2, 0, 9, 5, 5, 6, 6, 5, 3, 0, 4, 1, 6, 4, 8, 8, 7, 6, 0, 5, 1, 5, 5, 1, 0, 8, 3, 8, 6, 2, 6, 1, 2, 0, 8, 0, 8, 0, 0, 6, 8, 4, 2, 3, 0, 7, 9
OFFSET
1,1
LINKS
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
Cf. A114800 (n!8), A143280 (m(2)), A288055 (m(3)), A288091 (m(4)), A288092 (m(5)), A288093 (m(6)), A288094 (m(7)), this sequence (m(8)), A288096 (m(9)).
Sequence in context: A199781 A193117 A016677 * A231863 A179589 A368737
KEYWORD
nonn,cons
AUTHOR
STATUS
approved