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A327606
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Expansion of e.g.f. exp(x)*(1-x)*x/(1-2*x)^2.
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3
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0, 1, 8, 69, 712, 8705, 123456, 1994293, 36163184, 727518177, 16081980760, 387499155461, 10108673620728, 283851555270049, 8536572699232592, 273759055527114165, 9325469762472018016, 336282091434597013313, 12797935594025234906664, 512609204063389138693957
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f: exp(x)*(1-x)*x/(1-2*x)^2.
a(n) = Sum_{k=1..n} k * A326659(n,k).
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MAPLE
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a:= n-> n!*coeff(series(exp(x)*(1-x)*x/(1-2*x)^2, x, n+1), x, n):
seq(a(n), n=0..23);
# second Maple program:
a:= proc(n) option remember; `if`(n<3, n^3,
2*(n+2)*a(n-1)-(4*n-1)*a(n-2)+2*(n-2)*a(n-3))
end:
seq(a(n), n=0..23);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Exp[x](1-x)(x/(1-2x)^2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 15 2020 *)
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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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