A218387 Decimal expansion of the spanning tree constant of the square lattice.

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

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Anthony J. Guttmann, Spanning tree generating functions and Mahler measure, arXiv:1207.2815 [math-ph], 2012.

Formula

Equals the product of A006752 by A088538.

From Amiram Eldar, Jul 22 2020: (Start)

Equals 1 + Sum_{k>=1} (2*k-1)!!^2/((2*k)!!^2 * (2*k + 1)).

Equals Sum_{k>=0} binomial(2*k,k)^2/(16^k * (2*k + 1)). (End)

Example

1.1662436161232751205...

Maple

evalf(Catalan*4/Pi) ;

Mathematica

RealDigits[4*Catalan/Pi, 10, 100][[1]] (* G. C. Greubel, Aug 23 2018 *)

Prog

(PARI) default(realprecision, 100); 4*Catalan/Pi \\ G. C. Greubel, Aug 23 2018
(Magma) R:= RealField(100); 4*Catalan(R)/Pi(R); // G. C. Greubel, Aug 23 2018

Crossrefs

Cf. A006752 (Catalan), A088538 (4/Pi).

Sequence in context: A191504 A021155 A254245 * A178857 A003676 A369508

Adjacent sequences: A218384 A218385 A218386 * A218388 A218389 A218390

Keyword

cons,easy,nonn

Author

R. J. Mathar, Oct 27 2012

Status

approved