A362473 - OEIS

%I #12 Apr 22 2023 10:32:59

%S 1,1,1,1,25,601,9001,105001,1231441,24146641,740098801,22443260401,

%T 607394284201,16102368745321,497289446373721,19072987370400601,

%U 806135144596672801,33945128330918599201,1426006261391514829921,63478993000497055809121

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

%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(-4*x^4 * exp(4*x))/4) = ( -LambertW(-4*x^4 * exp(4*x))/(4*x^4) )^(1/4).

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-4*x^4*exp(4*x))/4)))

%Y Cf. A143768, A349562, A362472.

%Y Cf. A362393, A362482, A362491.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Apr 21 2023