A362393 - OEIS

%I #15 Apr 21 2023 05:45:59

%S 1,1,1,1,25,241,1441,6721,87361,1729729,24816961,270452161,3705324481,

%T 85344916801,1992230175937,38047293910081,709217112938881,

%U 17385498239168641,514103858592923521,14254662916125735553,366807994235438359681,10338786602768939575681

%N E.g.f. satisfies A(x) = exp(x + x^4 * A(x)).

%H Seiichi Manyama, <a href="/A362393/b362393.txt">Table of n, a(n) for n = 0..422</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: exp(x - LambertW(-x^4 * exp(x))) = -LambertW(-x^4 * exp(x))/x^4.

%F a(n) = n! * Sum_{k=0..floor(n/4)} (k+1)^(n-3*k-1) / (k! * (n-4*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^4*exp(x)))))

%Y Cf. A125500, A362392.

%Y Cf. A362431.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Apr 20 2023