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 A373651 #29 Aug 07 2024 03:39:26
%S A373651 1,3,18,70,285,1071,3948,14148,49815,172645,590898,2000934,6714799,
%T A373651 22358805,73947240,243114552,795083931,2588073201,8389033710,
%U A373651 27089339130,87174634239,279653734437,894553405452,2853968436900,9083209323825,28844069541651,91405399485078
%N A373651 Expansion of (1 - 2*x + 3*x^2)/(1 - 2*x - 3*x^2)^(5/2).
%F A373651 a(n) = binomial(n+2,2) * Sum_{k=0..n} binomial(n,k) * binomial(k,n-k).
%F A373651 a(n) = binomial(n+2,2) * A002426(n).
%F A373651 a(n) = A132885(n+4,2).
%F A373651 a(n) = ((n+2)/n^2) * ((2*n-1)*a(n-1) + 3*(n+1)*a(n-2)).
%o A373651 (PARI) my(N=30, x='x+O('x^N)); Vec((1-2*x+3*x^2)/(1-2*x-3*x^2)^(5/2))
%Y A373651 Cf. A002426, A132885, A144087.
%K A373651 nonn
%O A373651 0,2
%A A373651 _Seiichi Manyama_, Aug 06 2024