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 A370568 #31 Jun 09 2024 09:02:27
%S A370568 1,8,44,207,896,3689,14706,57361,220363,837430,3157440,11835916,
%T A370568 44176890,164355675,609981045,2259680355,8359285126,30890694534,
%U A370568 114059719703,420887785505,1552362630016,5723494732725,21096366345741,77742879583057,286445422547405
%N A370568 Expansion of g.f. (1-x) / (1-9*x+28*x^2-35*x^3+15*x^4-x^5).
%C A370568 The sequence is constructed from a truncated version of Pascal's Triangle. See A370074 for an example. a(n) arises from the Gambler's Ruin problem and represents the number of ways a gambler is ruined after starting with $8 with a maximum $11 causing retirement.
%H A370568 Paolo Xausa, <a href="/A370568/b370568.txt">Table of n, a(n) for n = 0..1000</a>
%H A370568 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-28,35,-15,1).
%F A370568 a(n) = 9*a(n-1)-28*a(n-2)+35*a(n-3)-15*a(n-4)+a(n-5) for n>=5.
%t A370568 LinearRecurrence[{9, -28, 35, -15, 1}, {1, 8, 44, 207, 896}, 25] (* _Paolo Xausa_, Jun 09 2024 *)
%Y A370568 Cf. A211216, A224422, A221863, A122588, A370074, A370051, A370391.
%K A370568 nonn,easy
%O A370568 0,2
%A A370568 _Peter Morris_, Feb 22 2024