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 A381911 #15 Mar 22 2025 10:16:32
%S A381911 1,2,9,55,394,3102,25969,226891,2045342,18883205,177640462,1696658418,
%T A381911 16408796013,160366113609,1581329919636,15713344659359,
%U A381911 157187582466527,1581676730708500,15998326150898211,162571286470135097,1658893916098102321,16991130941208846890
%N A381911 Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A001764.
%F A381911 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x*A(x)).
%F A381911 a(n) = Sum_{k=0..n} binomial(n+3*k+1,k) * binomial(2*n-k,n-k)/(n+3*k+1).
%t A381911 Table[Sum[Binomial[n + 3*k + 1, k] * Binomial[2*n - k, n - k]/(n + 3*k + 1), {k, 0, n}], {n, 0, 25}] (* _Vaclav Kotesovec_, Mar 22 2025 *)
%o A381911 (PARI) a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(2*n-k, n-k)/(n+3*k+1));
%Y A381911 Cf. A381912, A381913.
%Y A381911 Cf. A381817, A381914.
%Y A381911 Cf. A001764.
%K A381911 nonn
%O A381911 0,2
%A A381911 _Seiichi Manyama_, Mar 10 2025