A380028 Expansion of e.g.f. sqrt(1 - 2*x*exp(x)).
1, -1, -3, -12, -79, -760, -9561, -147994, -2716239, -57632040, -1387518625, -37365406606, -1112793904311, -36312032900884, -1288357188957489, -49380149141206290, -2033232328710195871, -89506187915127440560, -4194948681994077973377, -208545134727411799745878
Offset: 0
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[Sqrt[1-2x Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Apr 22 2025 *) -
PARI
a(n) = n!*sum(k=0, n, (-2)^k*k^(n-k)*binomial(1/2, k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} (-2)^k * k^(n-k) * binomial(1/2,k)/(n-k)!.