A362798 -id:A362798 - cp's OEIS frontend

A362795 E.g.f. satisfies A(x) = (1+x)^(A(x)^(x^2)).

1, 1, 0, 0, 24, 0, -60, 7980, -12992, -23184, 10320480, -54616320, 160009344, 33740939232, -391545030240, 3173349947040, 211401523687680, -4586955333880320, 66611949275370240, 2068372502060292864, -82278329345056212480, 1885659676128917982720

Offset: 0

Seiichi Manyama, May 04 2023

sign

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

Cf. A033917, A362794.

Cf. A362798, A362800.

my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x)^exp(-lambertw(-x^2*log(1+x)))))

E.g.f.: exp( -LambertW(-x^2 * log(1+x)) / x^2 ) = (1+x)^exp( -LambertW(-x^2 * log(1+x)) ).

E.g.f.: Sum_{k>=0} (k*x^2 + 1)^(k-1) * (log(1+x))^k / k!.

A362796 E.g.f. satisfies A(x) = 1/(1-x)^(A(x)^x).

Original entry on oeis.org

1, 1, 2, 12, 72, 650, 6480, 80906, 1121512, 18069264, 320204160, 6348340152, 136915211664, 3230148306216, 82078412377416, 2248247450065080, 65771634671679360, 2052879248516927232, 67955959831214467584, 2381716543764159438336

Offset: 0

Seiichi Manyama, May 04 2023

nonn

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

Cf. A052813, A362798.

Cf. A362794, A362799.

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

E.g.f.: exp( -LambertW(x * log(1-x)) / x ) = 1/(1-x)^exp( -LambertW(x * log(1-x)) ).

E.g.f.: Sum_{k>=0} (k*x + 1)^(k-1) * (-log(1-x))^k / k!.

A362800 E.g.f. satisfies A(x) = exp( (exp(x) - 1) * A(x)^(x^2) ).

Original entry on oeis.org

1, 1, 2, 5, 39, 292, 2063, 21877, 271372, 3298155, 47855035, 805112970, 13843621861, 261388560253, 5529798475178, 122059754102345, 2863956966387107, 73150334575839340, 1961833778207602123, 55184622355007805281, 1656027290812446938492

Offset: 0

Seiichi Manyama, May 04 2023

nonn

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

Cf. A052880, A362799.
Cf. A362795, A362798.
Cf. A000110, A362571.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x^2*(exp(x)-1))/x^2)))

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

E.g.f.: Sum_{k>=0} (k*x^2 + 1)^(k-1) * (exp(x) - 1)^k / k!.

cp's OEIS Frontend

A362795 E.g.f. satisfies A(x) = (1+x)^(A(x)^(x^2)).

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A362796 E.g.f. satisfies A(x) = 1/(1-x)^(A(x)^x).

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A362800 E.g.f. satisfies A(x) = exp( (exp(x) - 1) * A(x)^(x^2) ).

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