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A356952
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E.g.f. satisfies log(A(x)) = x^3/6 * (exp(x) - 1) * A(x).
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3
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1, 0, 0, 0, 4, 10, 20, 35, 1736, 15204, 88320, 415965, 7632460, 121801966, 1368227224, 12184672955, 176889193040, 3490851044360, 59703361471296, 837948141904569, 13407228541467540, 283596013866706450, 6226093732482731800, 121326684752194084471
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..floor(n/4)} (k+1)^(k-1) * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).
E.g.f.: A(x) = Sum_{k>=0} (k+1)^(k-1) * (x^3/6 * (exp(x) - 1))^k / k!.
E.g.f.: A(x) = exp( -LambertW(x^3/6 * (1 - exp(x))) ).
E.g.f.: A(x) = LambertW(x^3/6 * (1 - exp(x)))/(x^3/6 * (1 - exp(x))).
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MATHEMATICA
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nmax = 23; A[_] = 1;
Do[A[x_] = Exp[x^3/6*(Exp[x] - 1)*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
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PROG
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(PARI) a(n) = n!*sum(k=0, n\4, (k+1)^(k-1)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^(k-1)*(x^3/6*(exp(x)-1))^k/k!)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(x^3/6*(1-exp(x))))))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(x^3/6*(1-exp(x)))/(x^3/6*(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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