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E.g.f. satisfies A(x) = exp( x * (1+x)^4 * A(x) ).
1

%I #10 Sep 12 2024 07:49:45

%S 1,1,11,124,1997,42616,1120327,35203960,1288741337,53898829408,

%T 2536932089771,132770439164584,7649993702503429,481295935534882768,

%U 32834728249861856879,2414570451161244199576,190412665638185073399473,16030575396743899522805440

%N E.g.f. satisfies A(x) = exp( x * (1+x)^4 * 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)^4) ).

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

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

%Y Cf. A362771, A362772, A376145.

%Y Cf. A360082, A367790.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 11 2024