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A288092
Decimal expansion of m(5) = Sum_{n>=0} 1/n!5, the 5th reciprocal multifactorial constant.
10
3, 6, 4, 0, 2, 2, 4, 4, 6, 7, 7, 3, 3, 8, 0, 9, 7, 3, 4, 1, 7, 6, 9, 3, 7, 2, 3, 6, 9, 6, 3, 5, 6, 9, 0, 6, 0, 6, 3, 2, 4, 0, 9, 5, 1, 6, 9, 6, 8, 8, 4, 2, 5, 9, 9, 4, 5, 2, 9, 5, 5, 7, 6, 3, 0, 8, 3, 6, 6, 6, 5, 7, 3, 1, 3, 2, 8, 1, 4, 8, 5, 2, 5, 9, 0, 0, 6, 4, 4, 4, 1, 3, 9, 8, 6, 9, 1, 0, 1, 3, 5, 7
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
3.640224467733809734176937236963569060632409516968842599452955763...
MATHEMATICA
m[5] = (1/5)*E^(1/5)*(5 + 5^(1/5)*(Gamma[1/5] - Gamma[1/5, 1/5]) + 5^(2/5)*(Gamma[2/5] - Gamma[2/5, 1/5]) + 5^(3/5)*(Gamma[3/5] - Gamma[3/5, 1/5]) + 5^(4/5)*(Gamma[4/5] - Gamma[4/5, 1/5])); RealDigits[m[5], 10, 102][[1]]
PROG
(PARI) default(realprecision, 105); (1/5)*exp(1/5)*(5 + sum(k=1, 4, 5^(k/5)*(gamma(k/5) - incgam(k/5, 1/5)))) \\ G. C. Greubel, Mar 28 2019
(Magma) SetDefaultRealField(RealField(105)); (1/5)*Exp(1/5)*(5 + (&+[5^(k/5)*Gamma(k/5, 1/5): k in [1..4]])); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx((1/5)*exp(1/5)*(5 + sum(5^(k/5)*(gamma(k/5) - gamma_inc(k/5, 1/5)) for k in (1..4))), digits=105) # G. C. Greubel, Mar 28 2019
CROSSREFS
Cf. A085157 (n!5), A143280 (m(2)), A288055 (m(3)), A288091 (m(4)), this sequence (m(5)), A288093 (m(6)), A288094 (m(7)), A288095 (m(8)), A288096 (m(9)).
Sequence in context: A085881 A265480 A309084 * A127574 A356501 A334279
KEYWORD
nonn,cons
AUTHOR
STATUS
approved