A086053 Decimal expansion of Lengyel's constant L.

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

Offset

1,3

Comments

L - log(Pi-1)/log(2) ~ 0.00000171037285384 ~ 1/Pi^11.5999410273. - Gerald McGarvey, Aug 17 2004

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 319 and 556.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000

László Babai and Tamás Lengyel, A convergence criterion for recurrent sequences with application to the partition lattice, Analysis, Vol. 12, No. 1-2 (1992), pp. 109-120; preprint.

Tamás Lengyel, On a recurrence involving Stirling numbers, European Journal of Combinatorics, Vol. 5, No. 4 (1984), pp. 313-321.

Tamás Lengyel, On some 2-adic properties of a recurrence involving Stirling numbers, p-Adic Numbers Ultrametric Anal. Appl., Vol. 4, No. 3 (2012), pp. 179-186.

Simon Plouffe, The Lengyel constant.

Thomas Prellberg, On the asymptotic analysis of a class of linear recurrences (slides).

Eric Weisstein's World of Mathematics, Lengyel's Constant.

Formula

Equals lim_{n->oo} A005121(n) * (2*log(2))^n * n^(1+log(2)/3) / n!^2. - Amiram Eldar, Jun 27 2021

Example

1.0986858055251870130177463257213318079312220710644268407410427815783217...

Crossrefs

Cf. A005121, A131407, A330804, A331957.

Cf. A260932, A385521.

Sequence in context: A384059 A132721 A309948 * A358661 A129269 A094145

Adjacent sequences: A086050 A086051 A086052 * A086054 A086055 A086056

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 07 2003

Extensions

More terms from Vaclav Kotesovec, Mar 11 2014

Status

approved