cp's OEIS Frontend

A370391 Expansion of (1 - 2*x)/(1 - 9*x + 28*x^2 - 35*x^3 + 15*x^4 - x^5).

%I A370391 #43 Apr 04 2024 10:40:13
%S A370391 1,7,35,154,636,2533,9861,37810,143451,540155,2022735,7543771,
%T A370391 28048829,104050724,385320419,1425038684,5264963100,19437087382,
%U A370391 71715418017,264483764116,975070823122,3593840295815,13243217176106,48793364067681,179753027448972
%N A370391 Expansion of (1 - 2*x)/(1 - 9*x + 28*x^2 - 35*x^3 + 15*x^4 - x^5).
%C A370391 The sequence is constructed by a truncated version of Pascal's Triangle.
%C A370391                      1
%C A370391                   1     1
%C A370391                1     2     1
%C A370391             1     3     3     1
%C A370391          1     4     6     4
%C A370391       1     5    10    10     4
%C A370391    1     6    15    20    14
%C A370391       7    21    35    34    14
%C A370391    7    28    56    69    48
%C A370391      35    84   125   117    48
%C A370391   35   119   209   242   165
%C A370391                 ...
%C A370391 After truncation the sequence appears as the left vertical column. The right column sequence can be in A370051.
%C A370391 a(n) arises from the Gambler's Ruin problem and represents the number of ways a gambler is ruined after starting with $7 with a maximum $11 causing retirement.
%H A370391 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-28,35,-15,1).
%F A370391 a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5).
%t A370391 LinearRecurrence[{9, -28, 35, -15, 1}, {1, 7,35,154,636}, 25] (* _James C. McMahon_, Mar 12 2024 *)
%Y A370391 Cf. A211216, A224422, A221863, A122588, A370074, A370051.
%K A370391 nonn,easy
%O A370391 0,2
%A A370391 _Peter Morris_, Feb 22 2024