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A288094 Decimal expansion of m(7) = Sum_{n>=0} 1/n!7, the 7th reciprocal multifactorial constant. 10
3, 8, 8, 6, 9, 5, 9, 6, 5, 3, 7, 4, 0, 8, 4, 3, 4, 9, 5, 4, 2, 8, 5, 6, 9, 9, 1, 0, 9, 3, 6, 7, 0, 5, 6, 7, 2, 7, 0, 5, 3, 0, 9, 5, 8, 7, 5, 2, 0, 1, 6, 0, 4, 8, 5, 8, 0, 4, 3, 9, 5, 3, 3, 8, 6, 9, 1, 7, 0, 3, 7, 6, 2, 2, 7, 6, 7, 8, 4, 7, 3, 1, 7, 5, 6, 7, 6, 4, 0, 6, 0, 6, 4, 5, 8, 3, 0, 0, 1, 7, 4, 4, 7, 6 (list; constant; graph; refs; listen; history; text; internal format)
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
3.88695965374084349542856991093670567270530958752016048580439533869...
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[7], 10, 104][[1]]
RealDigits[Total[Table[1/Times@@Range[n, 1, -7], {n, 0, 500}]], 10, 120][[1]] (* Harvey P. Dale, May 21 2023 *)
PROG
(PARI) default(realprecision, 105); (1/7)*exp(1/7)*(7 + sum(k=1, 6, 7^(k/7)*(gamma(k/7) - incgam(k/7, 1/7)))) \\ G. C. Greubel, Mar 28 2019
(Magma) SetDefaultRealField(RealField(105)); (1/7)*Exp(1/7)*(7 + (&+[7^(k/7)*Gamma(k/7, 1/7): k in [1..6]])); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx((1/7)*exp(1/7)*(7 + sum(7^(k/7)*(gamma(k/7) - gamma_inc(k/7, 1/7)) for k in (1..6))), digits=105) # G. C. Greubel, Mar 28 2019
CROSSREFS
Cf. A114799 (n!7), A143280 (m(2)), A288055 (m(3)), A288091 (m(4)), A288092 (m(5)), A288093 (m(6)), this sequence (m(7)), A288095 (m(8)), A288096 (m(9)).
Sequence in context: A118817 A179553 A157471 * A131596 A332892 A371137
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)