A365040 -id:A365040 - cp's OEIS frontend

A365038 E.g.f. satisfies A(x) = exp(x * (1 + x)/A(x)).

1, 1, 1, -2, 9, -44, 175, 246, -21007, 396712, -5576769, 57840850, -151112951, -14137899060, 539212013327, -13335393617714, 239914650459105, -1990873438067504, -76974185162417921, 5220283004540970282, -194958036625254566599, 5226632355735840377140

Offset: 0

Seiichi Manyama, Aug 18 2023

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

Cf. A362771, A362773, A363478, A365039, A365040.

Cf. A361067.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(x*(1+x)))))

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

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

A365039 E.g.f. satisfies A(x) = exp(x * (1 + x)/A(x)^2).

Original entry on oeis.org

1, 1, -1, 7, -79, 1201, -22961, 530167, -14372191, 447825889, -15776617249, 620209389031, -26918670325295, 1278598424153233, -65973615445792081, 3674793950748867031, -219773335672937703871, 14046128883828030510529, -955409650156763223984449

Offset: 0

Seiichi Manyama, Aug 18 2023

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

Cf. A362771, A362773, A363478, A365038, A365040.

Cf. A361068.

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

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

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

cp's OEIS Frontend

A365038 E.g.f. satisfies A(x) = exp(x * (1 + x)/A(x)).

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