A069080 a(n) = (2n+1)*(2n+2)*(2n+6)*(2n+7).

84, 864, 3300, 8736, 18900, 35904, 62244, 100800, 154836, 228000, 324324, 448224, 604500, 798336, 1035300, 1321344, 1662804, 2066400, 2539236, 3088800, 3722964, 4449984, 5278500, 6217536, 7276500, 8465184, 9793764, 11272800, 12913236, 14726400, 16724004

Offset

0,1

References

Konrad Knopp, Theory and application of infinite series, Dover, p. 268.

Links

Table of n, a(n) for n=0..30.

Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")

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

Formula

Sum_{n>=0} (-1)^n/a(n) = (Pi-149/60)/60. [Corrected by Amiram Eldar, Mar 08 2022]

From Wesley Ivan Hurt, Mar 28 2015: (Start)

G.f.: 12*(7 + 37*x - 15*x^2 + 3*x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

a(n) = 16*n^4 + 128*n^3 + 332*n^2 + 304*n + 84. (End)

Sum_{n>=0} 1/a(n) = 49/3600. - Amiram Eldar, Mar 08 2022

Maple

A069080:=n->16*n^4 + 128*n^3 + 332*n^2 + 304*n + 84: seq(A069080(n), n=0..30); # Wesley Ivan Hurt, Mar 28 2015

Mathematica

CoefficientList[Series[12 (7 + 37x - 15x^2 + 3x^3)/(1 - x)^5, {x, 0, 30}], x] (* Wesley Ivan Hurt, Mar 28 2015 *)

Prog

(Magma) [(2*n+1)*(2*n+2)*(2*n+6)*(2*n+7) : n in [0..30]]; // Wesley Ivan Hurt, Mar 28 2015
(PARI) Vec(12*(7 + 37*x - 15*x^2 + 3*x^3) / (1 - x)^5 + O(x^50)) \\ Michel Marcus, Mar 29 2015
(PARI) vector(50, n, n--; (2*n+1)*(2*n+2)*(2*n+6)*(2*n+7)) \\ Michel Marcus, Mar 29 2015

Crossrefs

Sequence in context: A220016 A219827 A219719 * A219577 A093284 A027794

Adjacent sequences: A069077 A069078 A069079 * A069081 A069082 A069083

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 05 2002

Status

approved