A365035 -id:A365035 - cp's OEIS frontend

A365036 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^2)).

1, 1, 3, -5, -23, 521, -1829, -71021, 1319697, 5905297, -683965709, 8664974891, 311864420473, -13981842414695, 6694007756619, 16448800124183491, -448649039951220959, -13236887251789967071, 1210629233913421852387, -12065049302884271631269

Offset: 0

Seiichi Manyama, Aug 17 2023

sign

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

Cf. A125500, A143768, A363354, A363529, A365035, A365037.

Cf. A361091.

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

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

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

A365037 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^3)).

Original entry on oeis.org

1, 1, 3, -11, -11, 1341, -14339, -168923, 8905065, -85313735, -4604578919, 197455645641, -273728455571, -267002430142187, 9427821270512373, 178475402982086701, -28273343910563670959, 713736314833387866225, 51907546734507018043057

Offset: 0

Seiichi Manyama, Aug 17 2023

sign

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

Cf. A125500, A143768, A363354, A363529, A365035, A365036.

Cf. A361092.

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(3*x^2*exp(-3*x))/3)))

E.g.f.: exp( x + LambertW(3*x^2*exp(-3*x))/3 ).

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

cp's OEIS Frontend

A365036 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^2)).

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