A376145 - OEIS

%I #9 Sep 12 2024 07:49:52

%S 1,1,9,88,1265,23916,558427,15608986,508516017,18936594712,

%T 793902926771,37017671474334,1900666877186761,106576903636156084,

%U 6481047448001720427,424870924596413523106,29871349825140536394593,2242231079099137007066544

%N E.g.f. satisfies A(x) = exp( x * (1+x)^3 * A(x) ).

%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( -LambertW(-x * (1+x)^3) ).

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(1+x)^3))))

%Y Cf. A362771, A362772, A376146.

%Y Cf. A360076, A367789.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 11 2024