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 A372279 #17 Feb 16 2025 08:34:06
%S A372279 1,1,11,181,4461,148101,6202651,314158461,18682884681,1276509416761,
%T A372279 98552772971451,8485633118339301,806247602665104661,
%U A372279 83796784405535693181,9457590223483413296811,1151924494605809502276301,150602291336042725831941201
%N A372279 E.g.f. A(x) satisfies A(x) = exp( x * ( exp(x) * A(x) )^(5/2) ).
%H A372279 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372279 E.g.f.: A(x) = exp( -2/5 * LambertW(-5*x/2 * exp(5*x/2)) ).
%F A372279 E.g.f.: A(x) = ( -LambertW(-5*x/2 * exp(5*x/2)) / (5*x/2 * exp(5*x/2)) )^(2/5).
%F A372279 E.g.f.: A(x) = ( Sum_{k>=0} (k+1)^(k-1) * (5*x/2 * exp(5*x/2))^k / k! )^(2/5).
%F A372279 a(n) = Sum_{k=0..n} (5*k/2)^(n-k) * (5*k/2+1)^(k-1) * binomial(n,k).
%F A372279 a(n) ~ sqrt(1 + LambertW(exp(-1))) * 5^(n-1) * n^(n-1) / (exp(n - 2/5) * 2^(n-1) * LambertW(exp(-1))^n). - _Vaclav Kotesovec_, May 06 2024
%o A372279 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-2/5*lambertw(-5/2*x*exp(5*x/2)))))
%o A372279 (PARI) a(n) = sum(k=0, n, (5*k/2)^(n-k)*(5*k/2+1)^(k-1)*binomial(n, k));
%Y A372279 Cf. A273953, A273954, A360544, A360547.
%Y A372279 Cf. A372278.
%K A372279 nonn
%O A372279 0,3
%A A372279 _Seiichi Manyama_, Apr 25 2024