A196280 a(n) = binomial(n+9, 9)*8^n.

1, 80, 3520, 112640, 2928640, 65601536, 1312030720, 23991418880, 407854120960, 6525665935360, 99190122217472, 1442765414072320, 20198715797012480, 273459536944168960, 3594039628409077760, 46003707243636195328, 575046340545452441600, 7035861107850241638400

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (80,-2880,61440,-860160,8257536,-55050240,251658240,-754974720,1342177280,-1073741824).

Formula

a(n) = C(n+9,9)*8^n.

G.f.: 1 / (8*x-1)^10 . - R. J. Mathar, Oct 13 2011

From Amiram Eldar, Feb 17 2023: (Start)

Sum_{n>=0} 1/a(n) = 415065672*log(8/7) - 277121481/5.

Sum_{n>=0} (-1)^n/a(n) = 3099363912*log(9/8) - 12776837121/35. (End)

Mathematica

Table[Binomial[n+9, 9]8^n, {n, 0, 20}] (* or *) LinearRecurrence[{80, -2880, 61440, -860160, 8257536, -55050240, 251658240, -754974720, 1342177280, -1073741824}, {1, 80, 3520, 112640, 2928640, 65601536, 1312030720, 23991418880, 407854120960, 6525665935360}, 20] (* Harvey P. Dale, May 13 2017 *)

Prog

(Magma) [Binomial(n+9, 9)*8^n: n in [0..20]];

Crossrefs

Cf. A140406, A140802, A141054, A173155

Sequence in context: A035805 A017743 A234325 * A286789 A264372 A004390

Adjacent sequences: A196277 A196278 A196279 * A196281 A196282 A196283

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 13 2011

Status

approved