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 A056003 #35 Mar 22 2025 19:06:59
%S A056003 1,18,135,660,2475,7722,21021,51480,115830,243100,481338,906984,
%T A056003 1637610,2848860,4796550,7845024,12503007,19468350,29683225,44401500,
%U A056003 65270205,94427190,134617275,189329400,262957500,360988056,490217508,659002960,877549860,1158240600
%N A056003 a(n) = (n+1)*binomial(n+8, 8).
%C A056003 Original name: A second-order recursive sequence.
%D A056003 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A056003 Reinhard Zumkeller, <a href="/A056003/b056003.txt">Table of n, a(n) for n = 0..10000</a>
%H A056003 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A056003 G.f.: (1+8*x)/(1-x)^10.
%F A056003 a(n) = A245334(n+8,8)/A000142(8). - _Reinhard Zumkeller_, Aug 31 2014
%F A056003 From _Amiram Eldar_, Jan 15 2023: (Start)
%F A056003 Sum_{n>=0} 1/a(n) = 4*Pi^2/3 - 266681/22050.
%F A056003 Sum_{n>=0} (-1)^n/a(n) = 2*Pi^2/3 - 38656*log(2)/105 + 611409/2450. (End)
%p A056003 a:=n->(sum((numbcomp(n,9)), j=9..n)):seq(a(n), n=9..35); # _Zerinvary Lajos_, Aug 26 2008
%t A056003 a[n_] := (n+1)*Binomial[n+8, 8]; Array[a, 50, 0] (* _Amiram Eldar_, Jan 15 2023 *)
%o A056003 (Haskell)
%o A056003 a056003 n = (n + 1) * a007318' (n + 8) 8
%o A056003 -- _Reinhard Zumkeller_, Aug 31 2014
%o A056003 (PARI) a(n) = (n+1)*binomial(n+8, 8) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A056003 Partial sums of A056117.
%Y A056003 Cf. A093644 ((9, 1) Pascal, column m=9).
%Y A056003 Cf. A000142, A007318, A052206, A245334, A254142 (partial sums).
%K A056003 nonn,easy
%O A056003 0,2
%A A056003 _Barry E. Williams_, Jun 12 2000