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A362380
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E.g.f. satisfies A(x) = exp(x + 3*x^2/2 * A(x)).
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5
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1, 1, 4, 19, 154, 1456, 18136, 260002, 4430812, 85170988, 1854422236, 44693165716, 1188169271488, 34434053438968, 1082632555160248, 36666259172292016, 1331754793762045456, 51622725829298301520, 2127683533625205288400
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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.: exp(x - LambertW(-3*x^2/2 * exp(x))) = -2 * LambertW(-3*x^2/2 * exp(x))/(3*x^2).
a(n) = n! * Sum_{k=0..floor(n/2)} (3/2)^k * (k+1)^(n-k-1) / (k! * (n-2*k)!).
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MATHEMATICA
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nmax = 20; A[_] = 1;
Do[A[x_] = Exp[x + 3*x^2/2*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^2/2*exp(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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