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 A370106 #9 Feb 10 2024 09:23:42
%S A370106 1,1,-3,-17,-19,126,591,344,-5907,-22373,2122,280842,854063,-810692,
%T A370106 -13254552,-31693392,67250413,615932985,1101123015,-4368359919,
%U A370106 -28043889894,-33371056204,254637122506,1245324193704,693586015791,-13913192640499
%N A370106 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n,k) * binomial(3*n,n-k).
%F A370106 a(n) = [x^n] ( (1-x)^2 * (1+x)^3 )^n.
%F A370106 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x/((1-x)^2*(1+x)^3) ). See A370107.
%o A370106 (PARI) a(n) = sum(k=0, n, (-1)^k * binomial(2*n, k)*binomial(3*n, n-k));
%Y A370106 Cf. A234839, A368467.
%Y A370106 Cf. A370107.
%K A370106 sign
%O A370106 0,3
%A A370106 _Seiichi Manyama_, Feb 10 2024