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 A361142 #19 Mar 14 2023 03:41:57
%S A361142 1,1,7,91,1773,46401,1529593,60911103,2845757449,152663425633,
%T A361142 9250206248781,624880915165959,46569571425664477,3795729136868379777,
%U A361142 335902071304953561073,32074779600414913885231,3287242849289861637185937,359917016243351870997841473
%N A361142 E.g.f. satisfies A(x) = exp( x*A(x)^2/(1 - x*A(x)) ).
%H A361142 Winston de Greef, <a href="/A361142/b361142.txt">Table of n, a(n) for n = 0..338</a>
%F A361142 a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(n-1,n-k)/k!.
%F A361142 a(n) ~ s^2 * sqrt((2 - r*s)/(2 + r*s*(-2 + s*(2 - r*s)^2))) * n^(n-1) / (exp(n) * r^(n - 1/2)), where r = 0.14220768719194290600038416000340972911571484385125... and s = 1.549730657609106944767484487465870359529391502493... are roots of the system of equations exp(r*s^2/(1 - r*s)) = s, r*s^2*(2 - r*s) = (1 - r*s)^2. - _Vaclav Kotesovec_, Mar 03 2023
%t A361142 Table[n! * Sum[(n+k+1)^(k-1) * Binomial[n-1,n-k]/k!, {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 03 2023 *)
%o A361142 (PARI) a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(n-1, n-k)/k!);
%Y A361142 Cf. A000262, A361143.
%Y A361142 Cf. A052868, A052873, A161630.
%K A361142 nonn
%O A361142 0,3
%A A361142 _Seiichi Manyama_, Mar 02 2023