OFFSET
1,1
COMMENTS
Sequence could or should start with a(0) = 0. - M. F. Hasler, Sep 06 2025
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
Sum_{n>=1} 1/a(n) = 3*log(2) - 2 = A016631 - 2. (Ramanujan)
Sum_{n>=1} (-1)^(n+1)/a(n) = 2 - log(2) + sqrt(2)*log(sqrt(2)-1). - Amiram Eldar, Jun 24 2022
From Elmo R. Oliveira, Sep 05 2025: (Start)
G.f.: 3*x*(5 + 22*x + 5*x^2)/(x-1)^4.
E.g.f.: x*(15 + 48*x + 16*x^2)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
a(n) = A069140(n)/4. (End)
MATHEMATICA
Table[n(16n^2-1), {n, 40}] (* Harvey P. Dale, Dec 17 2018 *)
PROG
(PARI) a(n) = n*(16*n^2-1); \\ Michel Marcus, Nov 25 2013
(PARI) my(x='x+O('x^37)); Vec(3*x*(5+22*x+5*x^2)/(1-x)^4) \\ Elmo R. Oliveira, Sep 05 2025
(PARI) apply( {A069975(n)=n^3<<4-n}, [0..44]) \\ M. F. Hasler, Sep 06 2025
(Python) def A069975(n): return (n**3<<4)-n # M. F. Hasler, Sep 06 2025
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 30 2002
STATUS
approved