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A288094
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Decimal expansion of m(7) = Sum_{n>=0} 1/n!7, the 7th reciprocal multifactorial constant.
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10
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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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.
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EXAMPLE
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3.88695965374084349542856991093670567270530958752016048580439533869...
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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