A367790 -id:A367790 - cp's OEIS frontend

A367789 E.g.f. satisfies A(x) = exp( x/(1-x)^3 * A(x) ).

1, 1, 9, 106, 1697, 35076, 893947, 27165706, 960298593, 38751082552, 1758831242291, 88726543365054, 4926355857050641, 298605321687360676, 19623211558172733435, 1389870724939251455506, 105556814502357807727553, 8557797733469700008170224

Offset: 0

Seiichi Manyama, Nov 30 2023

nonn

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

Cf. A052868, A362775, A367790.

Cf. A091695, A360100.

A367789 := proc(n)
    n!*add((k+1)^(k-1) * binomial(n+2*k-1,n-k)/k!,k=0..n) ;
end proc:
seq(A367789(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

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

E.g.f.: exp( -LambertW(-x/(1-x)^3) ).

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

A376146 E.g.f. satisfies A(x) = exp( x * (1+x)^4 * A(x) ).

Original entry on oeis.org

1, 1, 11, 124, 1997, 42616, 1120327, 35203960, 1288741337, 53898829408, 2536932089771, 132770439164584, 7649993702503429, 481295935534882768, 32834728249861856879, 2414570451161244199576, 190412665638185073399473, 16030575396743899522805440

Offset: 0

Seiichi Manyama, Sep 11 2024

nonn

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

Cf. A362771, A362772, A376145.

Cf. A360082, A367790.

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

E.g.f.: exp( -LambertW(-x * (1+x)^4) ).

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

cp's OEIS Frontend

A367789 E.g.f. satisfies A(x) = exp( x/(1-x)^3 * A(x) ).

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