A289683 Mixing moments of the busy period of mean steady-state 1/2 in an M/M/1 waiting process.

1, 1, 3, 18, 171, 2250, 37935, 780570, 18967095, 531545490, 16877619675, 598825908450, 23479803807075, 1008211866111450, 47052981361160775, 2371481399995958250, 128370589834339227375, 7427764736129937449250, 457497972176819368669875

Offset

0,3

Links

Table of n, a(n) for n=0..18.

J. Abate, W. Whitt, Integer Sequences from Queueing Theory , J. Int. Seq. 13 (2010), 10.5.5, top of page 8.

Formula

a(n) = n!*b(n) where b(0)=1 and b(n) = Sum_{k=0..n-1}*binomial(n-1+k, n-1-k) *A000108(k) *(1/2)^k. [Abate, Eq. 15]

Conjecture: a(n) +2*(-2*n+3)*a(n-1) +(n-1)*(n-3)*a(n-2)=0. - R. J. Mathar, Jul 09 2017

Crossrefs

Sequence in context: A352649 A113130 A367373 * A193098 A322771 A177447

Adjacent sequences: A289680 A289681 A289682 * A289684 A289685 A289686

Keyword

nonn,easy

Author

R. J. Mathar, Jul 09 2017

Status

approved