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 A370074 #37 Apr 04 2024 10:39:38
%S A370074 1,3,9,28,90,297,1001,3432,11933,41971,149017,533141,1919215,6942950,
%T A370074 25215181,91858456,335449202,1227312350,4496994689,16496266812,
%U A370074 60566602692,222524531559,817997639090,3008175954887,11066005530460,40717739034761
%N A370074 Expansion of (1 - 2*x) * (1 - 4*x + 2*x^2) / (1 - 9*x + 28*x^2 - 35*x^3 + 15*x^4 - x^5).
%C A370074 The sequence is constructed from a truncated version of Pascal's Triangle.
%C A370074 1
%C A370074 1 1
%C A370074 1 2 1
%C A370074 3 3 1
%C A370074 3 6 4 1
%C A370074 9 10 5 1
%C A370074 9 19 15 6 1
%C A370074 28 34 21 7 1
%C A370074 28 62 55 28 8
%C A370074 90 117 83 36 8
%C A370074 90 207 200 119 44
%C A370074 297 407 319 163 44
%C A370074 ...
%C A370074 After truncation the sequence appears as the left vertical column. The right column sequence can be found in A370568. a(n) arises from the Gambler's Ruin problem and it represents the number of ways a gambler is ruined in the Gambler's Ruin problem starting with $3 and with a maximum $11 causing retirement.
%H A370074 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-28,35,-15,1).
%F A370074 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 A370074 LinearRecurrence[{9, -28, 35, -15, 1},{1,3,9,28,90},26] (* _James C. McMahon_, Mar 12 2024 *)
%Y A370074 Cf. A007318, A211216, A224422, A221863, A122588.
%K A370074 nonn,easy
%O A370074 0,2
%A A370074 _Peter Morris_, Feb 08 2024