A199300 a(n) = (2*n + 1)*7^n.

1, 21, 245, 2401, 21609, 184877, 1529437, 12353145, 98001617, 766718533, 5931980229, 45478515089, 346032180025, 2616003280989, 19668469112621, 147174406808233, 1096686708796833, 8142067989552245, 60251303122686613, 444556912229552577, 3271482918202092041

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (14,-49).

Formula

a(n) = 14*a(n-1) - 49*a(n-2).

G.f.: (1+7*x)/(1-7*x)^2.

a(n) = 7*a(n-1) + 2*7^n. - Vincenzo Librandi, Nov 05 2011

From Amiram Eldar, Dec 10 2022: (Start)

Sum_{n>=0} 1/a(n) = sqrt(7)*arccoth(sqrt(7)).

Sum_{n>=0} (-1)^n/a(n) = sqrt(7)*arccot(sqrt(7)). (End)

E.g.f.: exp(7*x)*(1 + 14*x). - Stefano Spezia, May 09 2023

Mathematica

a[n_] := (2*n + 1)*7^n; Array[a, 25, 0] (* Amiram Eldar, Dec 10 2022 *)

Prog

(Magma) [(2*n+1)*7^n: n in [0..30]]; // Vincenzo Librandi, Nov 05 2011
(PARI) a(n) = (2*n+1)*7^n \\ Amiram Eldar, Dec 10 2022

Crossrefs

Cf. A014480, A058962, A124647, A155988, A171220, A199299, A199301.

Sequence in context: A198974 A271792 A177730 * A302992 A344919 A165095

Adjacent sequences: A199297 A199298 A199299 * A199301 A199302 A199303

Keyword

nonn,easy

Author

Philippe Deléham, Nov 04 2011

Extensions

a(15) corrected by Vincenzo Librandi, Nov 05 2011

Status

approved