login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A133766
a(n) = (4*n+1)*(4*n+3)*(4*n+5).
4
15, 315, 1287, 3315, 6783, 12075, 19575, 29667, 42735, 59163, 79335, 103635, 132447, 166155, 205143, 249795, 300495, 357627, 421575, 492723, 571455, 658155, 753207, 856995, 969903, 1092315, 1224615, 1367187, 1520415, 1684683, 1860375, 2047875, 2247567, 2459835
OFFSET
0,1
REFERENCES
L. B. W. Jolley, Summation of Series, Dover, 1961.
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_{n>=0} 4/a(n) = (Pi-2)/4. [Jolley, eq. 238]
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Harvey P. Dale, May 06 2012
Sum_{n>=0} (-1)^n/a(n) = 1/8 + (log(2*sqrt(2)+3) - Pi)/(16*sqrt(2)). - Amiram Eldar, Feb 27 2022
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
Sequence in context: A105491 A158533 A284070 * A347980 A359404 A289951
KEYWORD
nonn,easy
AUTHOR
Miklos Kristof, Jan 02 2008
STATUS
approved