A288092 Decimal expansion of m(5) = Sum_{n>=0} 1/n!5, the 5th reciprocal multifactorial constant.

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

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

3.640224467733809734176937236963569060632409516968842599452955763...

Mathematica

m[5] = (1/5)*E^(1/5)*(5 + 5^(1/5)*(Gamma[1/5] - Gamma[1/5, 1/5]) + 5^(2/5)*(Gamma[2/5] - Gamma[2/5, 1/5]) + 5^(3/5)*(Gamma[3/5] - Gamma[3/5, 1/5]) + 5^(4/5)*(Gamma[4/5] - Gamma[4/5, 1/5])); RealDigits[m[5], 10, 102][[1]]

Prog

(PARI) default(realprecision, 105); (1/5)*exp(1/5)*(5 + sum(k=1, 4, 5^(k/5)*(gamma(k/5) - incgam(k/5, 1/5)))) \\ G. C. Greubel, Mar 28 2019
(Magma) SetDefaultRealField(RealField(105)); (1/5)*Exp(1/5)*(5 + (&+[5^(k/5)*Gamma(k/5, 1/5): k in [1..4]])); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx((1/5)*exp(1/5)*(5 + sum(5^(k/5)*(gamma(k/5) - gamma_inc(k/5, 1/5)) for k in (1..4))), digits=105) # G. C. Greubel, Mar 28 2019

Crossrefs

Cf. A085157 (n!5), A143280 (m(2)), A288055 (m(3)), A288091 (m(4)), this sequence (m(5)), A288093 (m(6)), A288094 (m(7)), A288095 (m(8)), A288096 (m(9)).

Sequence in context: A085881 A265480 A309084 * A127574 A356501 A334279

Adjacent sequences: A288089 A288090 A288091 * A288093 A288094 A288095

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 05 2017

Status

approved