A365037 -id:A365037 - cp's OEIS frontend

A365035 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).

1, 1, 3, 1, -11, 61, 301, -6299, 7561, 903673, -9019079, -145636919, 4305630781, 7516191541, -2037845181371, 22442805921901, 944219385367441, -29922880660473359, -288352494154313999, 32071808922904896913, -273044292430852251899

Offset: 0

Seiichi Manyama, Aug 17 2023

sign

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

Cf. A125500, A143768, A363354, A363529, A365036, A365037.

Cf. A361090.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(x^2*exp(-x)))))

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

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

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

Original entry on oeis.org

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!.

cp's OEIS Frontend

A365035 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).

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