STATUS
proposed
approved
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Revision History for A002627
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STATUS
editing
proposed
FORMULA
a(m) = int(Integral_{s=0..oo} ((1+s)^m - s^m)*exp(-s), s=0..infinity) = GAMMA(m+1,1) * exp(1) - GAMMA(m+1). - Stephen Crowley, Jul 24 2009
E.g.f.: Q(0)/(1-x), where Q(k)= 1 + (x-1)*k!/(1 - x/(x + (x-1)*(k+1)!/Q(k+1))); (continued fraction). (End)
(End)
Limit_{n -> infinityoo} a(n)/n! = exp(1) - 1. - Carmine Suriano, Jul 01 2015
STATUS
proposed
editing
STATUS
editing
proposed
LINKS
E. Elena Barcucci, A. Alberto Del Lungo , and R. Renzo Pinzani, <a href="http://dx.doi.org/10.1016/0304-3975(95)00199-9">"Deco" polyominoes, permutations and random generation</a>, Theoretical Computer Science, 159, 1996, 29-42.
J. Jimmy Devillet, <a href="https://arxiv.org/abs/1712.07856">Bisymmetric and quasitrivial operations: characterizations and enumerations</a>, [math.RA] arXiv:1712.07856 (2017).
DNicholas Kapoor and P. Singh, Christopher Staecker, <a href="https://arxiv.org/A002627abs/a0026272405.pdf09009The numbers LAhead of the Count: An Algorithm for Probabilistic Prediction of Instant Runoff (m,nIRV) and their relations with prepared Bernoulli and Eulerian numbersElections</a>, Math. Student, 20 (1952), 66-70arXiv:2405. 09009 [Annotated scanned copycs.CY], 2024. See p. 11.
Daljit Singh, <a href="/A002627/a002627.pdf">The numbers L(m,n) and their relations with prepared Bernoulli and Eulerian numbers</a>, Math. Student, 20 (1952), 66-70. [Annotated scanned copy]
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
LINKS
Jun Yan, <a href="https://arxiv.org/abs/2404.07958">Results on pattern avoidance in parking functions</a>, arXiv:2404.07958 [math.CO], 2024. See p. 5.
STATUS
approved
editing
PROG
(MAGMAMagma) I:=[1]; [0] cat [n le 1 select I[n] else n*Self(n-1)+1:n in [1..21]]; // Marius A. Burtea, Aug 07 2019