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 A382517 #12 Apr 02 2025 05:38:23
%S A382517 1,1,16,211,2611,31426,373099,4397527,51623530,604629688,7072089076,
%T A382517 82652922457,965513250832,11275328397061,131649767277064,
%U A382517 1536953772789256,17941954844917198,209439428952580837,2444747948094707815,28536537876362681194,333091044353156790346
%N A382517 Expansion of 1/(1 - x/(1 - 9*x)^(5/3)).
%F A382517 a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+2*k/3-1,n-k).
%F A382517 D-finite with recurrence (n-1)*(n-2)*a(n) -3*(19*n-37)*(n-2)*a(n-1) +27*(49*n^2-233*n+278)*a(n-2) +2*(-7655*n^2+39732*n-47656)*a(n-3) +3*(25519*n^2-98445*n-28306)*a(n-4) +54*(2552*n^2-69623*n+281314)*a(n-5) +27*(-137799*n^2+1870137*n-6193006)*a(n-6) +177147*(99*n^2-1323*n+4418)*a(n-7) -3188646*(3*n-20)*(3*n-22)*a(n-8)=0. - _R. J. Mathar_, Apr 02 2025
%o A382517 (PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(n+2*k/3-1, n-k));
%Y A382517 Cf. A362206, A362210, A382516.
%Y A382517 Cf. A004992.
%K A382517 nonn,easy
%O A382517 0,3
%A A382517 _Seiichi Manyama_, Mar 30 2025