A392026 Decimal expansion of 113*Pi + 355.

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, 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, 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

Offset

3,1

Comments

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.

Links

Table of n, a(n) for n=3..112.

D. H. Lehmer, Interesting Series Involving the Central Binomial Coefficient, The American Mathematical Monthly, 92:7 (1985), 449-457.

Formula

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

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

Equals 710 - 113 * A226043. - Amiram Eldar, Dec 27 2025

Example

709.9999698556466359462787...

Mathematica

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

Crossrefs

Cf. A014307, A068079, A180875, A226043.

Sequence in context: A335763 A096408 A005481 * A122699 A262807 A169603

Adjacent sequences: A392023 A392024 A392025 * A392027 A392028 A392029

Keyword

nonn,cons

Author

Artur Jasinski, Dec 27 2025

Status

approved