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A360465
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E.g.f. satisfies A(x) = exp(x * exp(2*x) * A(x)).
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3
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1, 1, 7, 64, 829, 14056, 295399, 7426252, 217637305, 7291538704, 275050426411, 11540336658676, 533224609095061, 26908386824872216, 1472691380336896399, 86892807951798473116, 5498668489586321670769, 371511527654280649783840
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: A(x) = exp( -LambertW(-x * exp(2*x)) ).
E.g.f.: A(x) = -LambertW(-x * exp(2*x)) / (x * exp(2*x)).
E.g.f.: A(x) = Sum_{k>=0} (k+1)^(k-1) * (x * exp(2*x))^k / k!.
a(n) = Sum_{k=0..n} (2*k)^(n-k) * (k+1)^(k-1) * binomial(n,k).
a(n) ~ sqrt(1+LambertW(2*exp(-1))) * 2^n * n^(n-1) / (exp(n-1) * LambertW(2*exp(-1))^n). - Vaclav Kotesovec, Feb 08 2023
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*exp(2*x)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-lambertw(-x*exp(2*x))/(x*exp(2*x))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^(k-1)*(x*exp(2*x))^k/k!)))
(PARI) a(n) = sum(k=0, n, (2*k)^(n-k)*(k+1)^(k-1)*binomial(n, k));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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