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A038159
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a(n) = n*a(n-1) + 1, a(0) = 2.
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4
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2, 3, 7, 22, 89, 446, 2677, 18740, 149921, 1349290, 13492901, 148421912, 1781062945, 23153818286, 324153456005, 4862301840076, 77796829441217, 1322546100500690, 23805829809012421, 452310766371236000, 9046215327424720001, 189970521875919120022
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OFFSET
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0,1
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LINKS
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FORMULA
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E.g.f.: (1+exp(x))/(1-x).
D-finite with recurrence: a(n) +(-n-1)*a(n-1) +(n-1)*a(n-2)=0. - R. J. Mathar, Feb 16 2014
0 = +a(n)*(+a(n+1) -3*a(n+2) +a(n+3)) +a(n+1)*(+a(n+1) -a(n+3)) +a(n+2)*(+a(n+2)) if n>=0. - Michael Somos, Oct 23 2017
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EXAMPLE
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G.f. = 2 + 3*x + 7*x^2+ 22*x^3 + 89*x^4 + 446*x^5 + 2677*x^6 + 18740*x^7 + ...
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MATHEMATICA
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a[ n_] := If[ n < 0, 0, n! SeriesCoefficient[ (1 + Exp[x]) / (1 - x), {x, 0, n}]] (* Michael Somos, Sep 04 2013 *)
Range[0, 20]! CoefficientList[Series[(1 + Exp[x])/(1 - x), {x, 0, 20}], x] (* Vincenzo Librandi, Feb 17 2014 *)
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PROG
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(PARI) {a(n) = if( n<0, 0, n! * sum(k=0, n, 1/k!, 1))}; /* Michael Somos, Sep 04 2013 */
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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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