A362321 - OEIS

%I #14 Feb 16 2025 08:34:05

%S 1,1,1,1,97,601,2161,5881,1303681,14723857,90770401,402581521,

%T 139389608161,2284512533161,19946635524817,122623661651401,

%U 57728368477678081,1240234284406887841,14010634784751445441,110117252571345122977

%N a(n) = n! * Sum_{k=0..floor(n/4)} n^k /(k! * (n-4*k)!).

%H Winston de Greef, <a href="/A362321/b362321.txt">Table of n, a(n) for n = 0..408</a>

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

%F a(n) = n! * [x^n] exp(x + n*x^4).

%F E.g.f.: exp( ( -LambertW(-4*x^4)/4 )^(1/4) ) / (1 + LambertW(-4*x^4)).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-4*x^4)/4)^(1/4))/(1+lambertw(-4*x^4))))

%Y Cf. A362301, A362323.

%K nonn,changed

%O 0,5

%A _Seiichi Manyama_, Apr 16 2023