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A351778
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Expansion of e.g.f. 1/(1 + 3*x*exp(x)).
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3
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1, -3, 12, -63, 420, -3435, 33462, -379155, 4903896, -71318259, 1152202290, -20474486043, 396890715636, -8334602179995, 188486823883134, -4567087352339235, 118039115079323952, -3241465018561379427, 94249758656850366186, -2892678859033260044043
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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} (-3)^(n-k) * (n-k)^k/k!.
a(0) = 1 and a(n) = -3 * 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+3x Exp[x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 21 2024 *)
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*exp(x))))
(PARI) a(n) = n!*sum(k=0, n, (-3)^(n-k)*(n-k)^k/k!);
(PARI) a(n) = if(n==0, 1, -3*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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