A016763 a(n) = (2*n+1)^11.

1, 177147, 48828125, 1977326743, 31381059609, 285311670611, 1792160394037, 8649755859375, 34271896307633, 116490258898219, 350277500542221, 952809757913927, 2384185791015625, 5559060566555523, 12200509765705829, 25408476896404831, 50542106513726817, 96549157373046875

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

G.f.: (1+x)*(x^10 +177134*x^9 +46525293*x^8 +1356555432*x^7 +9480267666*x^6 +19107752148*x^5 +9480267666*x^4 +1356555432*x^3 +46525293*x^2+ 177134*x +1)/(x-1)^12 . - R. J. Mathar, Jul 07 2017

From Amiram Eldar, Oct 11 2020: (Start)

Sum_{n>=0} 1/a(n) = 2047*zeta(11)/2048.

Sum_{n>=0} (-1)^n/a(n) = 50521*Pi^11/14863564800. (End)

Mathematica

Table[(2*n+1)^11, {n, 0, 20}] (* G. C. Greubel, Sep 15 2018 *)
LinearRecurrence[{12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1}, {1, 177147, 48828125, 1977326743, 31381059609, 285311670611, 1792160394037, 8649755859375, 34271896307633, 116490258898219, 350277500542221, 952809757913927}, 20] (* Harvey P. Dale, Nov 15 2020 *)

Prog

(Magma) [(2*n+1)^11: n in [0..20]]; // Vincenzo Librandi, Sep 07 2011
(Maxima) A016763(n):=(2*n+1)^11$
makelist(A016763(n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */
(PARI) vector(20, n, n--; (2*n+1)^11) \\ G. C. Greubel, Sep 15 2018

Crossrefs

Cf. A016751.

Sequence in context: A205177 A205276 A321827 * A016775 A016847 A016895

Adjacent sequences: A016760 A016761 A016762 * A016764 A016765 A016766

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved