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 A370105 #13 Feb 13 2024 10:56:20
%S A370105 1,3,23,192,1687,15253,140504,1311292,12357015,117318162,1120436273,
%T A370105 10752242592,103596191608,1001494496863,9709576926716,94369011385192,
%U A370105 919175964169623,8970063281146830,87685232945278010,858446087522807784,8415669293820893937
%N A370105 a(n) = Sum_{k=0..n} (-1)^k * binomial(n+k-1,k) * binomial(5*n-k-1,n-k).
%F A370105 a(n) = [x^n] 1/( (1+x) * (1-x)^4 )^n.
%F A370105 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x*(1+x)*(1-x)^4 ). See A365752.
%F A370105 a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1,k) * binomial(4*n-2*k-1,n-2*k).
%o A370105 (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k-1, k)*binomial(5*n-k-1, n-k));
%o A370105 (PARI) a(n, s=2, t=1, u=3) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
%Y A370105 Cf. A348410, A352373.
%Y A370105 Cf. A365752.
%K A370105 nonn
%O A370105 0,2
%A A370105 _Seiichi Manyama_, Feb 10 2024