A362655 -id:A362655 - cp's OEIS frontend

A362654 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x) ).

1, 1, 3, 22, 197, 2316, 33967, 595624, 12190761, 285479056, 7531645211, 221124649824, 7152276636397, 252742471065280, 9688895208298503, 400510408002257536, 17759663471017945553, 840937887639033467136, 42351198256293556043827

Offset: 0

Seiichi Manyama, Apr 28 2023

nonn

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

Cf. A273954, A362655.

Cf. A362653, A362673.

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)!).
a(n) ~ sqrt(1 + LambertW(2*exp(-2))) * 2^(n/2) * n^(n-1) / (exp(n-1) * LambertW(2*exp(-2))^(n/2)). - Vaclav Kotesovec, Aug 05 2025

A362661 E.g.f. satisfies A(x) = exp( x * exp(x^3/6) * A(x) ).

Original entry on oeis.org

1, 1, 3, 16, 129, 1356, 17767, 279714, 5149209, 108591688, 2582351451, 68380940904, 1995777685717, 63659665732716, 2203395556479951, 82253291389678756, 3294326092613575473, 140911264444599281616, 6411278790217738946899

Offset: 0

Seiichi Manyama, Apr 29 2023

nonn

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

Cf. A273954, A362660.

Cf. A143567, A354551, A362655.

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*exp(x^3/6)))))

E.g.f.: exp( -LambertW(-x * exp(x^3/6)) ).

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)^k * (n-3*k+1)^(n-3*k-1) / (6^k * k! * (n-3*k)!).

cp's OEIS Frontend

A362654 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x) ).

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