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 A386766 #15 Aug 03 2025 10:57:50
%S A386766 1,7,99,1618,28051,502182,9174174,169955268,3180814851,59997194782,
%T A386766 1138669104874,21718428172668,415955669988526,7994062687411132,
%U A386766 154087546950639324,2977629771383522568,57667991491752308451,1119034767346120619982,21752068061568290996274
%N A386766 a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * binomial(n+k-1,k).
%F A386766 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(2*n,k) * binomial(2*n-k-1,n-k).
%F A386766 a(n) = [x^n] ( (1+2*x)^2/(1-3*x) )^n.
%F A386766 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-3*x) / (1+2*x)^2 ). See A386772.
%F A386766 a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(2*n,k).
%F A386766 D-finite with recurrence 9*n*a(n) +6*(-18*n-5)*a(n-1) +80*(-17*n+37)*a(n-2) +800*(-2*n+5)*a(n-3)=0. - _R. J. Mathar_, Aug 03 2025
%o A386766 (PARI) a(n) = sum(k=0, n, 5^k*2^(n-k)*binomial(n+k-1, k));
%Y A386766 Cf. A386767, A386768.
%Y A386766 Cf. A386772.
%K A386766 nonn
%O A386766 0,2
%A A386766 _Seiichi Manyama_, Aug 02 2025