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
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).
Crossrefs
Cf. A016751.
Programs
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Magma
[(2*n+1)^11: n in [0..20]]; // Vincenzo Librandi, Sep 07 2011
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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 *) -
Maxima
A016763(n):=(2*n+1)^11$ makelist(A016763(n),n,0,20); /* Martin Ettl, Nov 12 2012 */
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PARI
vector(20, n, n--; (2*n+1)^11) \\ G. C. Greubel, Sep 15 2018
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)