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 A381983 #22 Mar 14 2025 08:59:05
%S A381983 1,2,15,280,8365,342566,17839339,1128217084,83987669721,7194842276842,
%T A381983 697216089189511,75408952092397760,9005278056681754885,
%U A381983 1176889697125038323662,167076740069554538243427,25603739419854491589361636,4212587964283017439802066353,740650326150658335888643004498
%N A381983 E.g.f. A(x) satisfies A(x) = exp(x) * C(x*A(x)^2), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
%F A381983 Let F(x) be the e.g.f. of A381997. F(x) = C(x*A(x)^2) = exp( 1/2 * Sum_{k>=1} binomial(2*k,k) * (x*A(x)^2)^k/k ).
%F A381983 a(n) = n! * Sum_{k=0..n} (2*k+1)^(n-k) * A002293(k)/(n-k)!.
%o A381983 (PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(n-k)*binomial(4*k+1, k)/((4*k+1)*(n-k)!));
%Y A381983 Cf. A349640, A381982.
%Y A381983 Cf. A000108, A002293, A381997.
%K A381983 nonn
%O A381983 0,2
%A A381983 _Seiichi Manyama_, Mar 11 2025