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A288093 Decimal expansion of m(6) = Sum_{n>=0} 1/n!6, the 6th reciprocal multifactorial constant.

%I A288093 #16 Apr 12 2025 05:18:28
%S A288093 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,
%T A288093 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,
%U A288093 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
%N A288093 Decimal expansion of m(6) = Sum_{n>=0} 1/n!6, the 6th reciprocal multifactorial constant.
%H A288093 G. C. Greubel, <a href="/A288093/b288093.txt">Table of n, a(n) for n = 1..10000</a>
%H A288093 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ReciprocalMultifactorialConstant.html">Reciprocal Multifactorial Constant</a>
%F A288093 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 A288093 3.771902396211758435660053589263943632646890281574478369567756485...
%t A288093 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]]
%o A288093 (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
%o A288093 (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
%o A288093 (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
%Y A288093 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)).
%K A288093 nonn,cons
%O A288093 1,1
%A A288093 _Jean-François Alcover_, Jun 05 2017