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A356906
E.g.f. satisfies A(x)^(A(x)^2) = 1/(1 - x)^x.
1
1, 0, 2, 3, -28, -150, 2154, 26040, -322512, -7872984, 77570280, 3752301960, -22068935736, -2542757920560, 1422846762960, 2302464947491800, 14860063644794880, -2653728770258072640, -41790782141846648640, 3739260018343338345600
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (-2*k+1)^(k-1) * |Stirling1(n-k,k)|/(n-k)!.
E.g.f.: A(x) = Sum_{k>=0} (-2*k+1)^(k-1) * (-x * log(1-x))^k / k!.
E.g.f.: A(x) = exp( LambertW(-2 * x * log(1-x))/2 ).
E.g.f.: A(x) = ( -2 * x * log(1-x)/LambertW(-2 * x * log(1-x)) )^(1/2).
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (-2*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-2*k+1)^(k-1)*(-x*log(1-x))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(-2*x*log(1-x))/2)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((-2*x*log(1-x)/lambertw(-2*x*log(1-x)))^(1/2)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 03 2022
STATUS
approved