A017458 a(n) = (11*n + 5)^10.

9765625, 1099511627776, 205891132094649, 6278211847988224, 79792266297612001, 604661760000000000, 3255243551009881201, 13744803133596058624, 48398230717929318249, 148024428491834392576

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), this sequence (m=10), A017459 (m=11), A017460 (m=12).

Programs

GAP

List([0..20], n-> (11*n+5)^10); # G. C. Greubel, Sep 19 2019

Magma

[(11*n+5)^10: n in [0..10]]; // Vincenzo Librandi, Sep 03 2011

Maple

seq((11*n+5)^10, n=0..20); # G. C. Greubel, Sep 19 2019

Mathematica

(11*Range[21] -6)^10 (* G. C. Greubel, Sep 19 2019 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{9765625,1099511627776,205891132094649,6278211847988224,79792266297612001,604661760000000000,3255243551009881201,13744803133596058624,48398230717929318249,148024428491834392576,404555773570791015625},20] (* Harvey P. Dale, Aug 19 2020 *)

PARI

vector(20, n, (11*n-6)^10) \\ G. C. Greubel, Sep 19 2019

Sage

[(11*n+5)^10 for n in (0..20)] # G. C. Greubel, Sep 19 2019

Formula

From G. C. Greubel, Sep 19 2019: (Start)

G.f.: (9765625 [phone]*x [phone]*x^2 +4073880923146640* x^3 +21874532039020442*x^4 +38639279895450554*x^5 +24069986191404704*x^6 +4993111339147592*x^7 [phone]*x^8 [phone]*x^9 [phone]* x^10)/(1-x)^11.

E.g.f.: (9765625 [phone]*x [phone]*x^2 [phone]* x^3 +2329598652561730*x^4 +2220242776827075*x^5 [phone]*x^6 + 214025260632480*x^7 [phone]*x^8 [phone]*x^9 [phone]* x^10)*exp(x). (End)