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A356949
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E.g.f. satisfies log(A(x)) = x^2 * (exp(x) - 1) * A(x).
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2
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1, 0, 0, 6, 12, 20, 1110, 7602, 35336, 1103832, 14984010, 134552990, 3457329612, 70828191876, 1017237973934, 25648737955050, 676111332667920, 13760810592066992, 373071111301807506, 11594147432172228918, 307097278689726728660, 9330499711181779575900
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * Stirling2(n-2*k,k)/(n-2*k)!.
E.g.f.: A(x) = Sum_{k>=0} (k+1)^(k-1) * (x^2 * (exp(x) - 1))^k / k!.
E.g.f.: A(x) = exp( -LambertW(x^2 * (1 - exp(x))) ).
E.g.f.: A(x) = LambertW(x^2 * (1 - exp(x)))/(x^2 * (1 - exp(x))).
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MATHEMATICA
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nmax = 21; A[_] = 1;
Do[A[x_] = Exp[(-1 + Exp[x])*A[x]*x^2] + O[x]^(nmax+1) // Normal, {nmax}];
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PROG
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(PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*stirling(n-2*k, k, 2)/(n-2*k)!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^(k-1)*(x^2*(exp(x)-1))^k/k!)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(x^2*(1-exp(x))))))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(x^2*(1-exp(x)))/(x^2*(1-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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