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A087912
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Expansion of exp(2*x/(1-x))/(1-x).
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0
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1, 3, 14, 86, 648, 5752, 58576, 671568, 8546432, 119401856, 1815177984, 29808908032, 525586164736, 9898343691264, 198227905206272, 4204989697906688, 94163381359509504, 2219240984918720512
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = n!*LaguerreL(n, -2).
a(n) = Sum_{k=0..n} 2^k*(n-k)!*binomial(n, k)^2.
E.g.f.: exp(x) * Sum_{n>=0} 2^n*x^n/n!^2 = Sum_{n>=0} a(n)*x^n/n!^2. [From Paul D. Hanna, Nov 18 2011]
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MAPLE
| a := proc(n) option remember: if n=0 then RETURN(1) fi: if n=1 then RETURN(1) fi: (2*n-1)*a(n-1) - (n-2)*(n-2)*a(n-2) end:for n from 1 to 18 do printf(`%d, `, a(n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 26 2006
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PROG
| {a(n)=n!^2*polcoeff(exp(x+x*O(x^n))*sum(m=0, n, 2^m*x^m/m!^2), n)} [From Paul D. Hanna, Nov 18 2011]
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CROSSREFS
| Sequence in context: A005189 A074520 A127715 * A051818 A091102 A132624
Adjacent sequences: A087909 A087910 A087911 * A087913 A087914 A087915
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 18 2003
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