A362774 E.g.f. satisfies A(x) = exp( x * (1+x)^2 * A(x)^2 ).

1, 1, 9, 115, 2265, 59701, 1981513, 79441167, 3736418801, 201790517833, 12309193580841, 837132560820139, 62809405894333321, 5154060532188515325, 459202970647825870313, 44146740571635016905991, 4555272678073789024849377, 502153774773932684443210513

Offset: 0

Author

Seiichi Manyama, May 02 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A361278, A362772.

Cf. A052750, A360547, A362776.

Programs

Maple

A362774 := proc(n)
    n!*add((2*k+1)^(k-1) * binomial(2*k,n-k)/k!,k=0..n) ;
end proc:
seq(A362774(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

PARI

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

Formula

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

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