A362674 -id:A362674 - cp's OEIS frontend

A362673 E.g.f. satisfies A(x) = exp( x * exp(x^2) / A(x) ).

1, 1, -1, 10, -51, 556, -7085, 116376, -2263303, 51072400, -1308626649, 37526799520, -1190440709051, 41385630158016, -1564585725985477, 63903022429837696, -2804097015221308815, 131558782973452677376, -6571623885587502740657

Offset: 0

Seiichi Manyama, Apr 29 2023

sign

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

Cf. A362674.

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

E.g.f.: exp( LambertW(x * exp(x^2)) ).

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

A362655 E.g.f. satisfies A(x) = exp( x * exp(x^3) * A(x) ).

Original entry on oeis.org

1, 1, 3, 16, 149, 1656, 22567, 369664, 7081209, 155178928, 3830958251, 105267080304, 3187172910517, 105437661606616, 3784329536385231, 146474021771040856, 6081955388047685873, 269686446704697314016, 12719466142269818201299

Offset: 0

Seiichi Manyama, Apr 28 2023

nonn

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

Cf. A273954, A362654.

Cf. A354553, A362674.

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

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

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

cp's OEIS Frontend

A362673 E.g.f. satisfies A(x) = exp( x * exp(x^2) / A(x) ).

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