A278300 Decimal expansion of a constant related to the asymptotics of A204249.

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 187.

Formula

Equals limit n->infinity (A204249(n)/(n!)^2)^(1/n).

Equals -2*LambertW(-1, -1/(2*exp(1/2)))^2 / (1 + 2*LambertW(-1, -1/(2*exp(1/2)))). - Vaclav Kotesovec, Jun 13 2021

Example

2.4554074822841279493757674026201760989493526408839235880697056011282...

Mathematica

RealDigits[-2*LambertW[-1, -1/(2*Exp[1/2])]^2 / (1 + 2*LambertW[-1, -1/(2*Exp[1/2])]), 10, 120][[1]] (* Vaclav Kotesovec, Jun 13 2021 *)

Crossrefs

Cf. A204249.

Sequence in context: A165044 A274079 A296372 * A034214 A317749 A253415

Adjacent sequences: A278297 A278298 A278299 * A278301 A278302 A278303

Keyword

nonn,cons

Author

Vaclav Kotesovec, Dec 01 2016

Extensions

More digits from Vaclav Kotesovec, Jun 13 2021

Status

approved