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A361212
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E.g.f. satisfies A(x) = exp( 3*x*A(x) / (1-x) ).
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2
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1, 3, 33, 612, 16353, 576108, 25306803, 1334701854, 82258866225, 5805344935368, 461848917299499, 40904277651802458, 3992219566916292873, 425766991650939828828, 49266876888419716251315, 6147944525591645916094182, 823045511075200872642258273
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..n} 3^k * (k+1)^(k-1) * binomial(n-1,n-k)/k!.
E.g.f.: exp ( -LambertW(-3*x/(1-x)) ).
E.g.f.: -(1-x)/(3*x) * LambertW(-3*x/(1-x)).
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PROG
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(PARI) a(n) = n!*sum(k=0, n, 3^k*(k+1)^(k-1)*binomial(n-1, n-k)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x/(1-x)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-(1-x)/(3*x)*lambertw(-3*x/(1-x))))
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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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