A377599 - OEIS

%I #81 Nov 14 2024 08:21:43

%S 1,2,13,145,2277,46461,1172713,35374697,1243296169,49940748073,

%T 2258238723021,113567169318285,6289161888870061,380364426242671469,

%U 24948313525570134001,1764095427822803465521,133782341347522663175889,10832097536377585282160337,932693691617428946786304661

%N E.g.f. satisfies A(x) = exp( x * A(x) / (1-x)^2 ) / (1-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) )/(1-x).

%F a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+2*k,n-k)/k!.

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

%o (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2*k, n-k)/k!);

%Y Cf. A367789, A377608, A377811.

%Y Cf. A361599.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 14 2024