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A372156
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E.g.f. A(x) satisfies A(x) = exp( 2 * x * (1 + x * A(x)^(1/2)) ).
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2
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1, 2, 8, 44, 328, 3032, 33964, 445580, 6727984, 114892784, 2192201044, 46233324788, 1068561369352, 26865052934696, 730137962157244, 21334636036296668, 667074635111434336, 22225983296836137440, 786215841115748129956, 29429693502599243538884
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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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E.g.f.: A(x) = exp( 2*x - 2*LambertW(-x^2 * exp(x)) ).
If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(s*k,n-k)/k!.
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*x-2*lambertw(-x^2*exp(x)))))
(PARI) a(n, r=2, s=1, t=0, u=1) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(s*k, n-k)/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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