A256323 - OEIS

%I #16 Feb 16 2025 08:33:25

%S 31,97,113,39,3781,257,3131,6791,6287,2113,33193,787,5933,2063,26827,

%T 16153,115453,11351,53107,92453,23677,3389,277777,52421,118127,99367,

%U 147971,82307,547381,4199,24659,365459,266719,72803,951481,172303,373591

%N a(n) = numerator of (1/n^3)*(-1/(n+1) + 16/(n+2) + 3/(4*(2*n+1)) - 81/(4*(2*n+3))), term of a BBP-type series representation of zeta(3) by V. Adamchik and S. Wagon.

%H Victor Adamchik and Stan Wagon, <a href="http://www.cs.cmu.edu/~adamchik/articles/pi/pi.htm">Pi: A 2000-Year Search Changes Direction</a>

%H David Bailey, Peter Borwein, Simon Plouffe, <a href="https://www.davidhbailey.com/dhbpapers/digits.pdf">On the rapid computation of various polylogarithmic constants</a>

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BBP-TypeFormula.html">BBP-Type Formula</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula">Bailey-Borwein-Plouffe formula</a>

%F a(n) = Numerator(1/n^3+1/(n+1)-2/(n+2)-6/(2*n+1)+6/(2*n+3)+1/n). - _Peter Luschny_, Mar 24 2015

%p a := n -> numer(1/n^3+1/(n+1)-2/(n+2)-6/(2*n+1)+6/(2*n+3)+1/n):

%p seq(a(n), n=1..37); # _Peter Luschny_, Mar 24 2015

%t a[n_] := Numerator[(1/n^3)*(-1/(n+1) + 16/(n+2) + 3/(4*(2*n+1)) - 81/(4*(2*n+3)))]; Table[a[n], {n, 1, 40}]

%o (Magma) [Numerator((1/n^3)*(-1/(n+1)+16/(n+2)+3/(4*(2*n+1))-81/(4*(2*n+3)))): n in [1..40]]; // _Vincenzo Librandi_, Mar 24 2015

%Y Cf. A002117, A256324 (denominators).

%K nonn,frac,easy

%O 1,1

%A _Jean-François Alcover_, Mar 24 2015