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 A381568 #18 Mar 01 2025 08:35:02 %S A381568 1,2,5,22,126,884,7149,64688,641836,6888740,79203860,968503090, %T A381568 12525131474,170555767116,2436592516874,36409825487380, %U A381568 567612675812796,9211031425896752,155283809480528788,2714788300934206360,49140787009610861896,919625415852055598804,17768937720619971300781 %N A381568 G.f. A(x) satisfies A(x) = (1 + x*A(x*A(x)))^2. %F A381568 See A381567. %F A381568 G.f.: B(x)^2, where B(x) is the g.f. of A143508. %o A381568 (PARI) a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n-2*j+2*k, j)/(n-j+k)*a(n-j, j))); %Y A381568 Column k=1 of A381567. %Y A381568 Cf. A087949, A120970, A143508, A381570. %K A381568 nonn %O A381568 0,2 %A A381568 _Seiichi Manyama_, Feb 28 2025