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 A045889 #14 Sep 22 2017 11:59:30
%S A045889 1,7,30,102,303,825,2116,5200,12381,28779,65658,147594,327835,721069,
%T A045889 1573056,3408084,7340265,15728895,33554710,71303470,150995271,
%U A045889 318767457,671089020,1409286552,2952790453,6174015955,12884902386
%N A045889 Partial sums of A045618.
%F A045889 a(n) = (n^2+11*n+34)/2 + (n-2)*2^(n+3).
%F A045889 G.f.: 1/((1-2*x)^2*(1-x)^3).
%F A045889 a(n) = Sum_{k=1..n+4} Sum_{i=1..n+4} (i-k) * C(n-k+4,i). - _Wesley Ivan Hurt_, Sep 19 2017
%t A045889 Table[(n^2 + 11 n + 34)/2 + (n - 2)*2^(n + 3), {n, 0, 26}] (* or *)
%t A045889 CoefficientList[Series[1/((1 - 2 x)^2*(1 - x)^3), {x, 0, 26}], x] (* _Michael De Vlieger_, Sep 21 2017 *)
%o A045889 (PARI) Vec(1/((1-2*x)^2*(1-x)^3) + O(x^40)) \\ _Michel Marcus_, Sep 20 2017
%Y A045889 Cf. A045618.
%K A045889 easy,nonn
%O A045889 0,2
%A A045889 _Wolfdieter Lang_