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A052845
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Expansion of e.g.f.: exp(x^2/(1-x)).
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16
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1, 0, 2, 6, 36, 240, 1920, 17640, 183120, 2116800, 26943840, 374220000, 5628934080, 91122071040, 1579034096640, 29155689763200, 571308920582400, 11838533804697600, 258608278645516800, 5938673374272038400, 143003892952893772800, 3602735624977961472000
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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D-finite with recurrence: a(0)=1, a(1)=0, a(2)=2, (n^2+3*n+2)*a(n)+(n^2+n-2)*a(n+1)+(-4-2*n)*a(n+2)+a(n+3)=0.
a(n) ~ n^(n-1/4)*exp(-3/2+2*sqrt(n)-n)/sqrt(2) * (1 + 43/(48*sqrt(n))). - Vaclav Kotesovec, Jun 24 2013, extended Dec 01 2021
E.g.f.: E(0) - 1, where E(k) = 2 + x^2/((2*k+1)*(1-x) - x^2/E(k+1) ); (continued fraction ). - Sergei N. Gladkovskii, Dec 30 2013
a(0) = 1; a(n) = Sum_{k=2..n} binomial(n-1,k-1) * k! * a(n-k). - Ilya Gutkovskiy, Feb 09 2020
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MAPLE
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spec := [S, {B=Sequence(Z, 1 <= card), C=Prod(Z, B), S= Set(C, 1 <= card)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Exp[x^2/(1-x)], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, May 31 2012 *)
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PROG
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(PARI)
N=33; x='x+O('x^N);
egf=exp(x^2/(1-x));
Vec(serlaplace(egf))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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Initial term changed to a(0) = 1, Apr 24 2005
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STATUS
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approved
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