A295240 -id:A295240 - cp's OEIS frontend

A295242 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - 2xexp(2x)/(1 - 3xexp(3x)/(1 - 4xexp(4x)/(1 - ...))))), a continued fraction.

1, 1, 8, 141, 4588, 238785, 18187146, 1907650213, 263668859560, 46443551748129, 10155810113182990, 2699369066774377701, 857103398097311042316, 320421972956640538172449, 139308015910536411839444194, 69693570411751759009119119685, 39753354051615620993914808710096

Offset: 0

Ilya Gutkovskiy, Nov 18 2017

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Cf. A295240, A295241.

nmax = 16; CoefficientList[Series[1/(1 + ContinuedFractionK[-k x Exp[k x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

a(n) ~ c * d^n * n^(2*n + 1/2) / exp(2*n), where d = 2.299007884747807311341155634117203393915283915595348... and c = 3.800670014949659244559370644121796775146171755... - Vaclav Kotesovec, Aug 09 2021

A295241 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - xexp(2x)/(1 - xexp(3x)/(1 - xexp(4*x)/(1 - ...))))), a continued fraction.

Original entry on oeis.org

1, 1, 6, 63, 1024, 23025, 671196, 24295537, 1059233008, 54376011009, 3229888525300, 218930722589601, 16744189595081928, 1431509929349664385, 135727622625718838092, 14175933450070804285665, 1621447178602905553394656, 202067106261905557292228097, 27312528199766157940311518436

Offset: 0

Ilya Gutkovskiy, Nov 18 2017

nonn

Cf. A295240, A295242.

nmax = 18; CoefficientList[Series[1/(1 + ContinuedFractionK[-x Exp[k x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

A347795 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - 4x*exp(x)/(1 - 9xexp(x)/(1 - 16xexp(x)/(1 - ...))))), a continued fraction.

Original entry on oeis.org

1, 1, 12, 429, 37876, 6761065, 2136044046, 1089769282777, 840138009989496, 930785292596431665, 1424838078730777692250, 2919980132606043561607201, 7805899106468938819037737572, 26636112093062499073393688363737, 113900544542333346101951507567405622

Offset: 0

Vaclav Kotesovec, Sep 14 2021

nonn

Cf. A295240.

nmax = 20; CoefficientList[Series[1/(1 + ContinuedFractionK[-k^2*x*Exp[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] * Range[0, nmax]!

a(n) ~ 2^(4*n + 7/2) * n^(3*n + 1) / (exp(3*n) * Pi^(2*n)).

cp's OEIS Frontend

A295242 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - 2xexp(2x)/(1 - 3xexp(3x)/(1 - 4xexp(4x)/(1 - ...))))), a continued fraction.

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A295241 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - xexp(2x)/(1 - xexp(3x)/(1 - xexp(4*x)/(1 - ...))))), a continued fraction.

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A347795 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - 4x*exp(x)/(1 - 9xexp(x)/(1 - 16xexp(x)/(1 - ...))))), a continued fraction.

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cp's OEIS Frontend

A295242 Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - 2*x*exp(2*x)/(1 - 3*x*exp(3*x)/(1 - 4*x*exp(4*x)/(1 - ...))))), a continued fraction.

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A295241 Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - x*exp(2*x)/(1 - x*exp(3*x)/(1 - x*exp(4*x)/(1 - ...))))), a continued fraction.

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A347795 Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - 4*x*exp(x)/(1 - 9*x*exp(x)/(1 - 16*x*exp(x)/(1 - ...))))), a continued fraction.

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A295242 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - 2xexp(2x)/(1 - 3xexp(3x)/(1 - 4xexp(4x)/(1 - ...))))), a continued fraction.

A295241 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - xexp(2x)/(1 - xexp(3x)/(1 - xexp(4*x)/(1 - ...))))), a continued fraction.

A347795 Expansion of e.g.f. 1/(1 - xexp(x)/(1 - 4x*exp(x)/(1 - 9xexp(x)/(1 - 16xexp(x)/(1 - ...))))), a continued fraction.