A017337 a(n) = (10*n + 5)^9.

1953125, 38443359375, 3814697265625, 78815638671875, 756680642578125, 4605366583984375, 20711912837890625, 75084686279296875, 231616946283203125, 630249409724609375, 1551328215978515625, 3517876291919921875, 7450580596923828125, 14893745087865234375, 28334269484119140625

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: 1953125*(x+1)*(x^8 + 19672*x^7 + 1736668*x^6 + 19971304*x^5 + 49441990*x^4 + 19971304*x^3 + 1736668*x^2 + 19672*x + 1)/(x-1)^10. -Colin Barker, Nov 13 2012

From Amiram Eldar, Apr 18 2023: (Start)

a(n) = A017329(n)^9.

a(n) = 5^9 * A016761(n).

Sum_{n>=0} 1/a(n) = 511*zeta(9)/1000000000.

Sum_{n>=0} (-1)^n/a(n) = 277*Pi^9/16128000000000. (End)

Mathematica

(10*Range[0, 20]+5)^9 (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1953125, 38443359375, 3814697265625, 78815638671875, 756680642578125, 4605366583984375, 20711912837890625, 75084686279296875, 231616946283203125, 630249409724609375}, 20] (* Harvey P. Dale, Jul 23 2016 *)

Prog

(Magma) [(10*n+5)^9: n in [0..15]]; // Vincenzo Librandi, Aug 02 2011

Crossrefs

Cf. A013667, A016761, A017329.

Sequence in context: A017049 A017133 A017229 * A017457 A017589 A308761

Adjacent sequences: A017334 A017335 A017336 * A017338 A017339 A017340

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved