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A288093
Decimal expansion of m(6) = Sum_{n>=0} 1/n!6, the 6th reciprocal multifactorial constant.
10
3, 7, 7, 1, 9, 0, 2, 3, 9, 6, 2, 1, 1, 7, 5, 8, 4, 3, 5, 6, 6, 0, 0, 5, 3, 5, 8, 9, 2, 6, 3, 9, 4, 3, 6, 3, 2, 6, 4, 6, 8, 9, 0, 2, 8, 1, 5, 7, 4, 4, 7, 8, 3, 6, 9, 5, 6, 7, 7, 5, 6, 4, 8, 5, 2, 5, 9, 6, 4, 3, 2, 9, 4, 5, 7, 4, 3, 8, 3, 8, 7, 0, 9, 3, 5, 2, 0, 3, 5, 8, 1, 0, 5, 1, 5, 3, 5, 6, 2, 2, 5, 5
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
3.771902396211758435660053589263943632646890281574478369567756485...
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[6], 10, 102][[1]]
PROG
(PARI) default(realprecision, 105); (1/6)*exp(1/6)*(6 + sum(k=1, 5, 6^(k/6)*(gamma(k/6) - incgam(k/6, 1/6)))) \\ G. C. Greubel, Mar 28 2019
(Magma) SetDefaultRealField(RealField(105)); (1/6)*Exp(1/6)*(6 + (&+[6^(k/6)*Gamma(k/6, 1/6): k in [1..5]])); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx((1/6)*exp(1/6)*(6 + sum(6^(k/6)*(gamma(k/6) - gamma_inc(k/6, 1/6)) for k in (1..5))), digits=105) # G. C. Greubel, Mar 28 2019
CROSSREFS
Cf. A085158 (n!6), A143280 (m(2)), A288055 (m(3)), A288091 (m(4)), A288092 (m(5)), this sequence (m(6)), A288094 (m(7)), A288095 (m(8)), A288096 (m(9)).
Sequence in context: A227336 A373862 A353049 * A131608 A131707 A348722
KEYWORD
nonn,cons
AUTHOR
STATUS
approved