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 A165618 #21 Mar 10 2022 07:57:27
%S A165618 0,8,44,164,494,1286,3002,6434,12869,24309,43757,75581,125969,203489,
%T A165618 319769,490313,735470,1081574,1562274,2220074,3108104,4292144,5852924,
%U A165618 7888724,10518299,13884155,18156203,23535819,30260339,38608019,48903491
%N A165618 a(n) = binomial(n+8,8) - 1.
%H A165618 Vincenzo Librandi, <a href="/A165618/b165618.txt">Table of n, a(n) for n = 0..1000</a>
%H A165618 E. Pérez Herrero, <a href="http://psychedelic-geometry.blogspot.com/2009/09/binomial-matrix-i.html">Binomial Matrix (I) partitions</a>, Psychedelic Geometry Blogspot, 09/22/09
%H A165618 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A165618 a(n) = binomial(n+8,8) - 1 = A000581(n+8) - 1.
%F A165618 a(n) = Sum_{r=1..n} binomial(8,r)*binomial(n,r).
%F A165618 a(n) = n(n+9)(n^6 + 27n^5 + 303n^4 + 1809n^3 + 6168n^2 + 11772n + 12176)/40320.
%t A165618 Table[ -1 + Binomial[n + 8, 8], {n, 0, 30}]
%t A165618 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,8,44,164,494,1286,3002,6434,12869},40] (* _Harvey P. Dale_, Nov 18 2013 *)
%o A165618 (PARI) vector(100,n,binomial(n+7,8)-1) \\ _Charles R Greathouse IV_, May 27 2011
%Y A165618 Cf. A000096, A000581, A062748, A063258, A062988, A124089, A124090, A035927.
%K A165618 nonn,easy
%O A165618 0,2
%A A165618 _Enrique Pérez Herrero_, Sep 22 2009
%E A165618 Edited by _Charles R Greathouse IV_, May 27 2011