OFFSET
0,1
REFERENCES
Jolley, Summation of Series, Dover (1961).
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: 3*(5 + 85*x + 39*x^2 - x^3)/(1-x)^4 .
E.g.f: (15 + 300*x + 336*x^2 + 64*x^3)*exp(x) .
sum(4/((4*m+1)*(4*m+3)*(4*m+5)), m=0..infinity) = (Pi-2)/4. [Jolley eq 238]
a(0)=15, a(1)=315, a(2)=1287, a(3)=3315; for n>3, a(n) = 4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). - Harvey P. Dale, May 06 2012
From Amiram Eldar, Feb 27 2022: (Start)
Sum_{n>=0} 1/a(n) = (Pi-2)/16.
Sum_{n>=0} (-1)^n/a(n) = 1/8 + (log(2*sqrt(2)+3) - Pi)/(16*sqrt(2)). (End)
MAPLE
seq((4*n+1)*(4*n+3)*(4*n+5), n=0..40);
MATHEMATICA
Table[c=4n; (c+1)(c+3)(c+5), {n, 0, 30}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {15, 315, 1287, 3315}, 30] (* Harvey P. Dale, May 06 2012 *)
PROG
(PARI) a(n)=(4*n+1)*(4*n+3)*(4*n+5) \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Miklos Kristof, Jan 02 2008
STATUS
editing