A288093 Decimal expansion of m(6) = Sum_{n>=0} 1/n!6, the 6th reciprocal multifactorial constant.

3, 7, 7, 1, 9, 0, 2, 3, 9, 6, 2, 1, 1, 7, 5, 8, 4, 3, 5, 6, 6, 0, 0, 5, 3, 5, 8, 9, 2, 6, 3, 9, 4, 3, 6, 3, 2, 6, 4, 6, 8, 9, 0, 2, 8, 1, 5, 7, 4, 4, 7, 8, 3, 6, 9, 5, 6, 7, 7, 5, 6, 4, 8, 5, 2, 5, 9, 6, 4, 3, 2, 9, 4, 5, 7, 4, 3, 8, 3, 8, 7, 0, 9, 3, 5, 2, 0, 3, 5, 8, 1, 0, 5, 1, 5, 3, 5, 6, 2, 2, 5, 5

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

3.771902396211758435660053589263943632646890281574478369567756485...

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[6], 10, 102][[1]]

Prog

(PARI) default(realprecision, 105); (1/6)*exp(1/6)*(6 + sum(k=1, 5, 6^(k/6)*(gamma(k/6) - incgam(k/6, 1/6)))) \\ G. C. Greubel, Mar 28 2019
(Magma) SetDefaultRealField(RealField(105)); (1/6)*Exp(1/6)*(6 + (&+[6^(k/6)*Gamma(k/6, 1/6): k in [1..5]])); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx((1/6)*exp(1/6)*(6 + sum(6^(k/6)*(gamma(k/6) - gamma_inc(k/6, 1/6)) for k in (1..5))), digits=105) # G. C. Greubel, Mar 28 2019

Crossrefs

Cf. A085158 (n!6), A143280 (m(2)), A288055 (m(3)), A288091 (m(4)), A288092 (m(5)), this sequence (m(6)), A288094 (m(7)), A288095 (m(8)), A288096 (m(9)).

Sequence in context: A227336 A373862 A353049 * A131608 A131707 A348722

Adjacent sequences: A288090 A288091 A288092 * A288094 A288095 A288096

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 05 2017

Status

approved