A200904 E.g.f. A(x) satisfies: A(x) = x*(2*exp(A(x)) - exp(2*A(x))).

1, 0, -6, -24, 170, 3420, 7126, -612528, -9539982, 84591300, 5635854158, 50835366648, -2827700267990, -99260514667860, 438301096424070, 118700423262570144, 2500018105640527586, -100537942668123244140, -6930391127610546125378, -31482610140761483476920

Offset

1,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..390

Formula

a(n) = Sum_{j=0..n} 2^j*(2*n-j)^(n-1)*(-1)^(n-j)*binomial(n,j), n > 0, a(0)=0.

Lim sup n->infinity (|a(n)|/n!)^(1/n) = abs(1/r) = 2.35574803651010217..., where r = 0.14939557933379789490 - 0.39733586552717789127*i is the complex root of the equation sqrt((r-2)*r) + 2*log(1/2 - sqrt((r-2)*r)/(2*r)) = 1+r, and i is the imaginary unit. - Vaclav Kotesovec, Jan 26 2014

Mathematica

Rest[CoefficientList[InverseSeries[Series[-(x/(E^x*(-2 + E^x))), {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 26 2014 *)
Table[Sum[2^j*(2*n-j)^(n-1)*(-1)^(n-j)*Binomial[n, j], {j, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec after Vladimir Kruchinin, Jan 26 2014 *)

Prog

(Maxima)
a(n):=(sum(2^j*(2*n-j)^(n-1)*(-1)^(n-j)*binomial(n, j), j, 0, n));

Crossrefs

Cf. A236466.

Sequence in context: A225827 A375627 A349498 * A293488 A038033 A064049

Adjacent sequences: A200901 A200902 A200903 * A200905 A200906 A200907

Keyword

sign

Author

Vladimir Kruchinin, Nov 23 2011

Status

approved