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 A352681 #11 Mar 29 2022 07:42:25 %S A352681 1,4,5,11,29,84,258,825,2717,9152,31382,109174,384370,1366936,4903140, %T A352681 17718165,64442205,235717800,866573070,3200179290,11865909990, %U A352681 44158628280,164881364700,617507304570,2319082988274,8731658843424,32953192276508,124635610132460 %N A352681 a(n) = [x^n] (3*x + 1)*(1 - sqrt(1 - 4*x))/(2*x). %F A352681 D-finite with recurrence a(n) = a(n-1)*((14*n + 2)*(2*n - 3))/((7*n - 6)*(n + 1)) for n >= 2. %F A352681 a(n) = A000108(n)+3*A000108(n-1). - _R. J. Mathar_, Mar 29 2022 %p A352681 alias(PS = ListTools:-PartialSums): %p A352681 aList := proc(len) local a, k, P, T; a := 4; P := [1]; T := [1]; %p A352681 for k from 0 to len-1 do T := [op(T), a]; P := PS([op(P), a]); a := P[-1] od; %p A352681 T end: aList(27); %p A352681 # Alternative: %p A352681 a := proc(n) option remember; if n = 0 then 1 elif n = 1 then 4 else %p A352681 a(n-1)*((14*n + 2)*(2*n - 3))/((7*n - 6)*(n + 1)) fi end: seq(a(n), n = 0..27); %Y A352681 a(n) = A352680(4, n). %K A352681 nonn,easy %O A352681 0,2 %A A352681 _Peter Luschny_, Mar 27 2022