A288094 - OEIS

A288094

Decimal expansion of m(7) = Sum_{n>=0} 1/n!7, the 7th reciprocal multifactorial constant.

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

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A288091 A288092 A288093 * A288095 A288096 A288097

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Jun 05 2017

STATUS

approved