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A189487
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Expansion of e.g.f. exp(x*exp(x) + x^2*exp(2*x)).
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1
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1, 1, 5, 28, 185, 1456, 13267, 135598, 1528193, 18805240, 250522451, 3585332554, 54774501025, 888739031116, 15249006695483, 275641537989766, 5231788966650113, 103968303762747472, 2157673505603964643, 46656574558459795522, 1049037051211541521121
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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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a(n) = n!*sum(m=1..n, sum(k=m..n, (k^(n-k)*binomial(m,k-m))/(n-k)!)/m!), n>0, a(0)=1.
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[x Exp[x]+x^2 Exp[2x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Sep 22 2011 *)
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PROG
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(Maxima)
a(n):=n!*sum(sum((k^(n-k)*binomial(m, k-m))/(n-k)!, k, m, n)/m!, m, 1, n);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(x)+x^2*exp(2*x)))) \\ Seiichi Manyama, Jul 17 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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