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A218387
Decimal expansion of the spanning tree constant of the square lattice.
9
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
Anthony J. Guttmann, Spanning tree generating functions and Mahler measure, arXiv:1207.2815 [math-ph], 2012.
Sheldon Yang, Some properties of Catalan's constant G, Internat. J. Math. Ed. Sci. Tech. 23 (4) (1992) 549-556, L*(1).
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
KEYWORD
cons,easy,nonn
AUTHOR
R. J. Mathar, Oct 27 2012
STATUS
approved