A362654 -id:A362654 - cp's OEIS frontend

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

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)!).

A362653 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x)^2 ).

Original entry on oeis.org

1, 1, 5, 55, 849, 17641, 462373, 14651295, 545025281, 23291218801, 1124589371301, 60553038168679, 3597677815336465, 233810179507710105, 16499939198003013509, 1256544674435523638671, 102713141497515307408257, 8970278754666722087785825

Offset: 0

Seiichi Manyama, Apr 28 2023

nonn

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

Cf. A360547, A362654, A362673.

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

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

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (2*n-4*k+1)^(n-2*k-1) / (k! * (n-2*k)!).

A362660 E.g.f. satisfies A(x) = exp( x * exp(x^2/2) * A(x) ).

Original entry on oeis.org

1, 1, 3, 19, 161, 1791, 24847, 413449, 8036625, 178852753, 4486426091, 125279093259, 3854964555697, 129618443364463, 4728625129171959, 186034319795094481, 7851808690935373793, 353903271319498588641, 16966669198377512202643

Offset: 0

Seiichi Manyama, Apr 29 2023

nonn

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

Cf. A273954, A362661.

Cf. A354550, A362654.

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

E.g.f.: exp( -LambertW(-x * exp(x^2/2)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (n-2*k+1)^(n-2*k-1) / (2^k * k! * (n-2*k)!).
a(n) ~ sqrt(1 + LambertW(exp(-2))) * n^(n-1) / (exp(n-1) * LambertW(exp(-2))^(n/2)). - Vaclav Kotesovec, Aug 05 2025

cp's OEIS Frontend

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

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A362653 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x)^2 ).

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A362660 E.g.f. satisfies A(x) = exp( x * exp(x^2/2) * A(x) ).

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