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A351777
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Expansion of e.g.f. 1/(1 + 2*x*exp(x)).
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2
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1, -2, 4, -6, -8, 150, -972, 3682, 6256, -289746, 3300460, -21071622, -27876312, 3156947014, -53217341660, 494232431250, 175171749088, -113735274256290, 2613309376750812, -32653995355358678, 36013529538641560, 10227377502146048118, -305630239215263764076
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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} (-2)^(n-k) * (n-k)^k/k!.
a(0) = 1 and a(n) = -2 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[1/(1+2x Exp[x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 06 2024 *)
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PROG
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(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1+2*x*exp(x))))
(PARI) a(n) = n!*sum(k=0, n, (-2)^(n-k)*(n-k)^k/k!);
(PARI) a(n) = if(n==0, 1, -2*n*sum(k=0, n-1, binomial(n-1, k)*a(k)));
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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