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A206304 E.g.f. is series reversion of x-log(1+x)^2 1
1, 2, 6, 22, 80, 128, -2940, -63072, -932088, -11628648, -114829968, -417677856, 21173151792, 869103962400, 23125766258208, 492858262277472, 7960636847682816, 46152793911618432, -3484964629275707328, -212667378331722666240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(n)= ((n-1)!*sum(k=0..n-1, binomial(n+k-1,n-1)*sum(j=0..k, binomial(k,j)*sum(i=0..j, ((-1)^(i)*binomial(j,i)*(2*(j-i))!*stirling1(n+j-i-1,2*(j-i)))/(n+j-i-1)!)))), n>0.

Lim sup n->infinity (|a(n)|/n!)^(1/n) = 1/abs((1+LambertW(-1/2))^2) = 1.57356815308645229... - Vaclav Kotesovec, Jan 22 2014

MATHEMATICA

Rest[CoefficientList[InverseSeries[Series[x-Log[1+x]^2, {x, 0, 20}], x], x]*Range[0, 20]!] (* Vaclav Kotesovec, Jan 22 2014 *)

PROG

(Maxima) a(n):= ((n-1)!*sum(binomial(n+k-1, n-1)*sum(binomial(k, j)*sum(((-1)^(i)*binomial(j, i)*(2*(j-i))!*stirling1(n+j-i-1, 2*(j-i)))/(n+j-i-1)!, i, 0, j), j, 0, k), k, 0, n-1));

CROSSREFS

Cf. A185151.

Sequence in context: A106434 A150228 A203038 * A201372 A072547 A150229

Adjacent sequences:  A206301 A206302 A206303 * A206305 A206306 A206307

KEYWORD

sign

AUTHOR

Vladimir Kruchinin, Feb 06 2012

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)