A365055 E.g.f. satisfies A(x) = exp( x * (1+x/2) * A(x)^3 ).

1, 1, 8, 121, 2818, 89006, 3559504, 172489948, 9825889532, 643567980808, 47654835126436, 3936868360416476, 358990055621209984, 35816155847478234424, 3880967272702222156952, 453886307361640406266456, 56985342864303337121933584, 7644651551838264804179619200

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..331

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: exp( -LambertW(-3*x * (1+x/2))/3 ).

a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (3*k+1)^(k-1) * binomial(k,n-k)/k!.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x*(1+x/2))/3)))

Crossrefs

Cf. A365053, A365054, A365056.

Cf. A363478.

Sequence in context: A298997 A299664 A243942 * A196651 A197456 A196341

Adjacent sequences: A365052 A365053 A365054 * A365056 A365057 A365058

Keyword

nonn

Author

Seiichi Manyama, Aug 19 2023

Status

approved