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 A364938 #14 Nov 18 2023 05:16:23
%S A364938 1,1,7,73,1141,23821,623341,19650793,725478601,30714824377,
%T A364938 1467394945561,78103975313101,4583805610661245,294093243091237669,
%U A364938 20479664124384110101,1538423857251845781841,124007828871708989798161,10676865465119963987425009
%N A364938 E.g.f. satisfies A(x) = exp( x / (1 - x*A(x))^3 ).
%F A364938 a(n) = n! * Sum_{k=0..n} (n-k+1)^(k-1) * binomial(n+2*k-1,n-k)/k!.
%F A364938 a(n) ~ sqrt(s*(1 + 2*r*s) / (4 + 3*r - 12*r*s + 12*r^2*s^2 - 4*r^3*s^3)) * n^(n-1) / (exp(n) * r^n), where r = 0.1811100305436879929789759231994897963241226689... and s = 1.893740207738561813713992833266450862854198944672... are real roots of the system of equations exp(r/(1 - r*s)^3) = s, 3*s*r^2 = (1 - r*s)^4. - _Vaclav Kotesovec_, Nov 18 2023
%t A364938 Join[{1}, Table[n! * Sum[(n-k+1)^(k-1) * Binomial[n+2*k-1,n-k]/k!, {k,0,n}], {n,1,20}]] (* _Vaclav Kotesovec_, Nov 18 2023 *)
%o A364938 (PARI) a(n) = n!*sum(k=0, n, (n-k+1)^(k-1)*binomial(n+2*k-1, n-k)/k!);
%Y A364938 Cf. A161630, A161635.
%Y A364938 Cf. A364940, A364942, A364981.
%K A364938 nonn
%O A364938 0,3
%A A364938 _Seiichi Manyama_, Aug 14 2023