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a(n) = (9*n + 11)*binomial(n+10, 10)/11.
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%I #25 Sep 08 2022 08:45:01

%S 1,20,174,988,4277,15288,47320,130832,330174,772616,1696396,3527160,

%T 6995534,13312768,24426552,43385360,74847175,125777340,206390730,

%U 331405620,521690715,806403000,1225732560,1834391520,2706007980,3938612496,5661434520,8043259504

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

%H T. D. Noe, <a href="/A056128/b056128.txt">Table of n, a(n) for n = 0..1000</a>

%H <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 a(n) = (9*n + 11)*binomial(n+10, 10)/11.

%F G.f.: (1+8*x)/(1-x)^12.

%F a(n) = 9*binomial(n+11,11) - 8*binomial(n+10,10). - _G. C. Greubel_, Jan 18 2020

%p seq( (9*n+11)*binomial(n+10, 10)/11, n=0..30); # _G. C. Greubel_, Jan 18 2020

%t CoefficientList[Series[(1+8x)/(1-x)^12, {x,0,40}], x] (* _Vincenzo Librandi_, Jul 30 2014 *)

%t 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 (Magma) [((9*n+11)*Binomial(n+10,10))/11: n in [0..40]]; // _Vincenzo Librandi_, Jul 30 2014

%o (PARI) vector(31, n, (9*n-2)*binomial(n+9,10)/11 ) \\ _G. C. Greubel_, Jan 18 2020

%o (Sage) [(9*n+11)*binomial(n+10,10)/11 for n in (0..30)] # _G. C. Greubel_, Jan 18 2020

%o (GAP) List([0..30], n-> (9*n+11)*Binomial(n+10,10)/11 ); # _G. C. Greubel_, Jan 18 2020

%Y Cf. A056003.

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Jul 08 2000

%E New name, from existing formula, added by _G. C. Greubel_, Jan 18 2020