cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A056128 a(n) = (9*n + 11)*binomial(n+10, 10)/11.

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%I A056128 #25 Sep 08 2022 08:45:01
%S A056128 1,20,174,988,4277,15288,47320,130832,330174,772616,1696396,3527160,
%T A056128 6995534,13312768,24426552,43385360,74847175,125777340,206390730,
%U A056128 331405620,521690715,806403000,1225732560,1834391520,2706007980,3938612496,5661434520,8043259504
%N A056128 a(n) = (9*n + 11)*binomial(n+10, 10)/11.
%H A056128 T. D. Noe, <a href="/A056128/b056128.txt">Table of n, a(n) for n = 0..1000</a>
%H A056128 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A056128 a(n) = (9*n + 11)*binomial(n+10, 10)/11.
%F A056128 G.f.: (1+8*x)/(1-x)^12.
%F A056128 a(n) = 9*binomial(n+11,11) - 8*binomial(n+10,10). - _G. C. Greubel_, Jan 18 2020
%p A056128 seq( (9*n+11)*binomial(n+10, 10)/11, n=0..30); # _G. C. Greubel_, Jan 18 2020
%t A056128 CoefficientList[Series[(1+8x)/(1-x)^12, {x,0,40}], x] (* _Vincenzo Librandi_, Jul 30 2014 *)
%t A056128 LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1}, {1,20,174, 988,4277,15288,47320,130832,330174,772616,1696396,3527160}, 40] (* _Harvey P. Dale_, Jan 14 2015 *)
%o A056128 (Magma) [((9*n+11)*Binomial(n+10,10))/11: n in [0..40]]; // _Vincenzo Librandi_, Jul 30 2014
%o A056128 (PARI) vector(31, n, (9*n-2)*binomial(n+9,10)/11 ) \\ _G. C. Greubel_, Jan 18 2020
%o A056128 (Sage) [(9*n+11)*binomial(n+10,10)/11 for n in (0..30)] # _G. C. Greubel_, Jan 18 2020
%o A056128 (GAP) List([0..30], n-> (9*n+11)*Binomial(n+10,10)/11 ); # _G. C. Greubel_, Jan 18 2020
%Y A056128 Cf. A056003.
%K A056128 easy,nonn
%O A056128 0,2
%A A056128 _Barry E. Williams_, Jul 08 2000
%E A056128 New name, from existing formula, added by _G. C. Greubel_, Jan 18 2020