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A288095 Decimal expansion of m(8) = Sum_{n>=0} 1/n!8, the 8th reciprocal multifactorial constant.

%I A288095 #17 Apr 12 2025 05:18:20
%S A288095 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,
%T A288095 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,
%U A288095 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
%N A288095 Decimal expansion of m(8) = Sum_{n>=0} 1/n!8, the 8th reciprocal multifactorial constant.
%H A288095 G. C. Greubel, <a href="/A288095/b288095.txt">Table of n, a(n) for n = 1..10000</a>
%H A288095 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ReciprocalMultifactorialConstant.html">Reciprocal Multifactorial Constant</a>
%F A288095 m(k) = (1/k)*exp(1/k)*(k + Sum_{j=1..k-1} k^(j/k)*(gamma(j/k) - gamma(j/k, 1/k))) where gamma(x) is the Euler gamma function and gamma(a,x) the incomplete gamma function.
%e A288095 3.9892412126901365441336421348019099438359273924576814826209556653...
%t A288095 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]]
%o A288095 (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
%o A288095 (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
%o A288095 (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
%Y A288095 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)).
%K A288095 nonn,cons
%O A288095 1,1
%A A288095 _Jean-François Alcover_, Jun 05 2017