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A288096
Decimal expansion of m(9) = Sum_{n>=0} 1/n!9, the 9th reciprocal multifactorial constant.
10
4, 0, 8, 1, 3, 7, 5, 5, 2, 0, 1, 6, 8, 8, 9, 8, 5, 4, 4, 0, 7, 1, 1, 0, 5, 1, 4, 6, 6, 0, 9, 6, 1, 0, 6, 9, 4, 6, 2, 6, 4, 1, 0, 0, 7, 7, 3, 1, 8, 6, 0, 7, 5, 8, 8, 4, 3, 4, 8, 5, 1, 7, 5, 1, 6, 7, 4, 9, 3, 4, 8, 7, 6, 3, 9, 0, 3, 3, 3, 5, 9, 9, 2, 1, 0, 5, 4, 2, 4, 2, 3, 0, 5, 7, 2, 0, 3, 5, 9, 0, 7, 4
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
4.08137552016889854407110514660961069462641007731860758843485175...
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[9], 10, 102][[1]]
PROG
(PARI) default(realprecision, 105); (1/9)*exp(1/9)*(9 + sum(k=1, 8, 9^(k/9)*(gamma(k/9) - incgam(k/9, 1/9)))) \\ G. C. Greubel, Mar 28 2019
(Magma) SetDefaultRealField(RealField(105)); (1/9)*Exp(1/9)*(9 + (&+[9^(k/9)*Gamma(k/9, 1/9): k in [1..8]])); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx((1/9)*exp(1/9)*(9 + sum(9^(k/9)*(gamma(k/9) - gamma_inc(k/9, 1/9)) for k in (1..8))), digits=105) # G. C. Greubel, Mar 28 2019
CROSSREFS
Cf. A114806 (n!9), A143280 (m(2)), A288055 (m(3)), A288091 (m(4)), A288092 (m(5)), A288093 (m(6)), A288094 (m(7)), A288095 (m(8)) this sequence (m(9)).
Sequence in context: A114401 A304440 A073467 * A021249 A010638 A123961
KEYWORD
nonn,cons
AUTHOR
STATUS
approved