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.
%I A056114 #33 Jan 15 2023 02:38:32
%S A056114 1,20,165,880,3575,12012,35035,91520,218790,486200,1016158,2015520,
%T A056114 3821090,6963880,12257850,20920064,34730575,56241900,89049675,
%U A056114 138138000,210315105,314757300,463681725,673171200,964177500,1363732656,1906401420,2636011840,3607704980
%N A056114 Expansion of (1+9*x)/(1-x)^11.
%D A056114 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A056114 T. D. Noe, <a href="/A056114/b056114.txt">Table of n, a(n) for n = 0..1000</a>
%H A056114 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A056114 a(n) = (n+1)*binomial(n+9, 9).
%F A056114 G.f.: (1+9*x)/(1-x)^11.
%F A056114 a(n) = A245334(n+9,9)/A000142(9). - _Reinhard Zumkeller_, Aug 31 2014
%F A056114 From _G. C. Greubel_, Jan 18 2020: (Start)
%F A056114 a(n) = 10*binomial(n+10,10) - 9*binomial(n+9,9).
%F A056114 E.g.f.: (9! +6894720*x +22861440*x^2 +26853120*x^3 +14605920*x^4 + 4191264*x^5 +677376*x^6 +63072*x^7 +3321*x^8 +91*x^9 +x^10)*exp(x)/9!. (End)
%F A056114 From _Amiram Eldar_, Jan 15 2023: (Start)
%F A056114 Sum_{n>=0} 1/a(n) = 3*Pi^2/2 - 1077749/78400.
%F A056114 Sum_{n>=0} (-1)^n/a(n) = 3*Pi^2/4 - 24576*log(2)/35 + 37652469/78400. (End)
%p A056114 a:=n->(sum((numbcomp(n,10)), j=10..n)):seq(a(n), n=10..34); # _Zerinvary Lajos_, Aug 26 2008
%t A056114 CoefficientList[Series[(1+9x)/(1-x)^11,{x,0,40}],x] (* or *) LinearRecurrence[ {11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,20,165,880,3575,12012,35035, 91520,218790,486200,1016158},40] (* _Harvey P. Dale_, Jun 05 2018 *)
%o A056114 (Haskell)
%o A056114 a056114 n = (n + 1) * a007318' (n + 9) 9
%o A056114 -- _Reinhard Zumkeller_, Aug 31 2014
%o A056114 (PARI) vector(41, n, n*binomial(n+8, 9) ) \\ _G. C. Greubel_, Jan 18 2020
%o A056114 (Magma) [(n+1)*Binomial(n+9, 9): n in [0..40]]; // _G. C. Greubel_, Jan 18 2020
%o A056114 (Sage) [(n+1)*binomial(n+9, 9) for n in (0..40)] # _G. C. Greubel_, Jan 18 2020
%o A056114 (GAP) List([0..40], n-> (n+1)*Binomial(n+9, 9)); # _G. C. Greubel_, Jan 18 2020
%Y A056114 Cf. A000142, A007318, A056003, A245334.
%K A056114 nonn,easy
%O A056114 0,2
%A A056114 _Barry E. Williams_, Jun 12 2000