A392026 - OEIS

%I #26 Jan 02 2026 13:52:24

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

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

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

%N Decimal expansion of 113*Pi + 355.

%C For a given exponent k, Sum_{m>=1} m^k*2^m/binomial(2*m,m) = (r/2)*Pi + s where r = A014307(k+1) and s = A180875(k), and the present constant is k=4, and r/(2*s) ~ Pi.

%H D. H. Lehmer, <a href="https://doi.org/10.1080/00029890.1985.11971651">Interesting Series Involving the Central Binomial Coefficient</a>, The American Mathematical Monthly, 92:7 (1985), 449-457.

%F Equals Sum_{m>=1} m^4*2^m/binomial(2*m, m).

%F Equals HypergeometricPFQ({2, 2, 2, 2, 2}, {1, 1, 1, 3/2}, 1/2).

%F Equals 710 - 113 * A226043. - _Amiram Eldar_, Dec 27 2025

%e 709.9999698556466359462787...

%t RealDigits[113 Pi + 355, 10, 110][[1]]

%Y Cf. A014307, A068079, A180875, A226043.

%K nonn,cons

%O 3,1

%A _Artur Jasinski_, Dec 27 2025