A016815 -id:A016815 - cp's OEIS frontend

A377558 Decimal expansion of Pi^3/64 + 7*zeta(3)/16.

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

Offset: 1

Stefano Spezia, Nov 01 2024

			1.01037296826200719010420286858471867099445163674...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 42.

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 40.

Cf. A002117, A016813, A016815, A091925, A233091, A377557, A377559, A377560.

RealDigits[Pi^3/64+7Zeta[3]/16,10,100][[1]]

Equals Sum_{k>=0} 1/(4*k + 1)^3 (see Finch).
Equals -psi''(1/4)/128 = -(psi''(1/8) + psi''(5/8))/1024 (see Shamos).
Equals hypergeom([1/4, 1/4, 1/4, 1], [5/4, 5/4, 5/4], 1). - R. J. Mathar, Jul 14 2025

A017091 a(n) = (8*n + 2)^3.

Original entry on oeis.org

8, 1000, 5832, 17576, 39304, 74088, 125000, 195112, 287496, 405224, 551368, 729000, 941192, 1191016, 1481544, 1815848, 2197000, 2628072, 3112136, 3652264, 4251528, 4913000, 5639752, 6434856, 7301384, 8242408, 9261000, 10360232, 11543176, 12812904, 14172488, 15625000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A002117, A016815, A017089 (8n+2), A000578 (n^3).

[(8*n+2)^3: n in [0..35]]; // Vincenzo Librandi, Jul 12 2011

(8*Range[0,30]+2)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{8,1000,5832,17576},30] (* Harvey P. Dale, Dec 30 2019 *)

G.f.: 8*(1 + 121*x + 235*x^2 + 27*x^3)/(x-1)^4. - R. J. Mathar, Jul 14 2016
From Amiram Eldar, Apr 24 2023: (Start)
a(n) = A017089(n)^3.
a(n) = 2^3*A016815(n).
Sum_{n>=0} 1/a(n) = Pi^3/512 + 7*zeta(3)/128. (End)

cp's OEIS Frontend

A377558 Decimal expansion of Pi^3/64 + 7*zeta(3)/16.

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