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A200904 E.g.f. A(x) satisfies: A(x) = x*(2*exp(A(x)) - exp(2*A(x))). 2
1, 0, -6, -24, 170, 3420, 7126, -612528, -9539982, 84591300, 5635854158, 50835366648, -2827700267990, -99260514667860, 438301096424070, 118700423262570144, 2500018105640527586, -100537942668123244140, -6930391127610546125378, -31482610140761483476920 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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: A359693 A225827 A349498 * A293488 A038033 A064049
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Nov 23 2011
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)