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

Author

Eric W. Weisstein, Jul 07 2003

Keywords

• nonn
• cons

Comments

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

Examples

			1.0986858055251870130177463257213318079312220710644268407410427815783217...
		

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.

Crossrefs

Cf. A005121, A131407, A330804, A331957.

Cf. A260932, A385521.

Formula

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

Extensions

More terms from Vaclav Kotesovec, Mar 11 2014