OFFSET
0,2
COMMENTS
Partial sums of A010014. - Jani Melik, May 20 2013
Terms end in the repeating sequence 1, 7, 5, 3, 9, ... - Melvin Peralta, Jul 08 2015
REFERENCES
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Marc Chamberland and Armin Straub, On gamma quotients and infinite products, Advances in Applied Mathematics, Vol. 51, No. 5 (2013), pp. 546-562.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
Sum_{n >= 0} 1/a(n) = 7 * zeta(3) / 8.
G.f.: (1+23*x+23*x^2+x^3)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 02 2012
E.g.f.: exp(x)*(1 + 26*x + 36*x^2 + 8*x^3). See A154537, row n=3. - Wolfdieter Lang, Mar 12 2017
From Bruce J. Nicholson, Dec 08 2019: (Start)
Sum_{n>=0} (-1)^n/a(n) = Pi^3/32 (A153071). - Amiram Eldar, Oct 10 2020
Product_{n>=1} (1 - (-1)^n/a(n)) = (Pi/12)*(1 + sqrt(2)*cosh(sqrt(3)*Pi/4)) (Chamberland and Straub, 2013). - Amiram Eldar, Jan 26 2024
MATHEMATICA
Range[1, 101, 2]^3 (* Harvey P. Dale, Nov 18 2013 *)
PROG
(Magma) [(2*n+1)^3: n in [0..50]]; // Vincenzo Librandi, Sep 05 2011
(PARI) a(n)=(2*n+1)^3 \\ Charles R Greathouse IV, Jan 02 2012
(Python)
def a(n): return (2*n+1)**3
print([a(n) for n in range(38)]) # Michael S. Branicky, Jan 27 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved