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 A382516 #11 Mar 31 2025 06:09:47
%S A382516 1,1,13,151,1693,18688,204631,2230498,24246229,263112874,2852058448,
%T A382516 30892668295,334454025715,3619669508056,39164977065622,
%U A382516 423695451762664,4583082589819489,49570596449054509,536121822834121354,5798064369702626227,62702959640721355228
%N A382516 Expansion of 1/(1 - x/(1 - 9*x)^(4/3)).
%F A382516 a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+k/3-1,n-k).
%F A382516 D-finite with recurrence (n-1)*(n-2)*a(n) -3*(n-2)*(17*n-35)*a(n-1) +27*(39*n^2-197*n+252)*a(n-2) +2*(-5468*n^2+32199*n-46873)*a(n-3) +6*(9115*n^2-56514*n+77702)*a(n-4) +54*(-1094*n^2-359*n+28901)*a(n-5) +54*(-9846*n^2+134559*n-449254)*a(n-6) +177147*(3*n-19)*(3*n-20)*a(n-7)=0. - _R. J. Mathar_, Mar 31 2025
%o A382516 (PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(n+k/3-1, n-k));
%Y A382516 Cf. A362206, A362210, A382517.
%Y A382516 Cf. A004991.
%K A382516 nonn,easy
%O A382516 0,3
%A A382516 _Seiichi Manyama_, Mar 30 2025