A001546 a(n) = (8*n+1)*(8*n+3)*(8*n+5)*(8*n+7).

105, 19305, 156009, 606825, 1666665, 3728745, 7284585, 12924009, 21335145, 33304425, 49716585, 71554665, 99900009, 135932265, 180929385, 236267625, 303421545, 383964009, 479566185, 591997545, 723125865, 874917225, 1049436009, 1248844905, 1475404905

Offset

0,1

Comments

From Jaume Oliver Lafont, May 30 2010: (Start)

3 divides a(n).

Sum_{k>=0} 1/a(k) = Pi/(96*(2+sqrt(2))) = 0.0095849081719... [Jolley eq. 243] (End)

References

Jolley, Summation of Series, Dover (1961).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: -3*(35+6260*x+20178*x^2+6260*x^3+35*x^4)/(x-1)^5. [Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4. - Wesley Ivan Hurt, Jan 02 2017

Maple

A001546:=n->(8*n+1)*(8*n+3)*(8*n+5)*(8*n+7): seq(A001546(n), n=0..50); # Wesley Ivan Hurt, Jan 02 2017

Mathematica

Table[Times@@(8n + {1, 3, 5, 7}), {n, 0, 30}] (* Harvey P. Dale, Jan 09 2011 *)

Prog

(PARI) a(n)=(8*n+1)*(8*n+3)*(8*n+5)*(8*n+7) \\ Charles R Greathouse IV, Oct 03 2011
(Magma) [(8*n+1)*(8*n+3)*(8*n+5)*(8*n+7): n in [0..20]]; // Vincenzo Librandi, Oct 04 2011

Crossrefs

Sequence in context: A094075 A199519 A082368 * A111647 A368513 A295463

Adjacent sequences: A001543 A001544 A001545 * A001547 A001548 A001549

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved