A236466 E.g.f. A(x) satisfies A(x) = x*(2*exp(A(x)) + exp(2*A(x))).

3, 24, 450, 13464, 555210, 29218212, 1871592534, 141327100080, 12293325631602, 1210526420471100, 133114686648358734, 16168770752009690376, 2149972767937717220394, 310628961824895629954388, 48456042707642573220000390, 8116814004435897170203179360

Offset

1,1

Links

Table of n, a(n) for n=1..16.

Formula

a(n) ~ sqrt(s/(3-2*s)) * n^(n-1) / (exp(n) * r^n), where s = 0.6693241011832267063... is the root of the equation (2-1/s)*(2+exp(s)) = 2, and r = s*exp(-s)/(2+exp(s)) = 0.08670317777647875508... - Vaclav Kotesovec, Jan 26 2014

Mathematica

Rest[CoefficientList[InverseSeries[Series[(x/(E^x*(2+E^x))), {x, 0, 20}], x], x]*Range[0, 20]!]
Table[Sum[2^j*(2*n-j)^(n-1)*Binomial[n, j], {j, 0, n}], {n, 1, 20}]

Crossrefs

Cf. A200904.

Sequence in context: A065761 A002832 A233151 * A185970 A279165 A336577

Adjacent sequences: A236463 A236464 A236465 * A236467 A236468 A236469

Keyword

nonn

Author

Vaclav Kotesovec, Jan 26 2014

Status

approved