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A009940
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Form the iterate f[ f[ .. f[ 1 ] ] ] or f^n [ 1 ] with f[ stuff ] defined as ( stuff - Integrate[ stuff over x ] ), set x=1 and multiply by n!.
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6
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1, 0, -1, -4, -15, -56, -185, -204, 6209, 112400, 1520271, 19165420, 237686449, 2944654296, 36392001815, 441823808804, 5066513855745, 49021548330016, 202510138910239, -8592616658156580, -399625593156546319
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| E.g.f.: exp(x/(x-1))/(1-x); a(n)=2*(n-1)*a(n-1)-(n-1)^2*a(n-2) for n>1, a(0)=1, a(1)=0; a(n)=n!*Laguerre(n, 1). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004
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EXAMPLE
| The first few f[ x ] are 1, 1 - x, 1 - 2*x + x^2/2, 1 - 3*x + (3*x^2)/2 - x^3/6, giving the values 1, 0, -1/2, -2/3, ...
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MAPLE
| seq(coeff(convert(series(exp(x/(x-1))/(1-x), x, 50), polynom), x, i)*i!, i=0..20); A009940:=proc(n) options remember: if n<2 then RETURN([1, 0][n+1]) else RETURN(2*(n-1)*A009940(n-1)-(n-1)^2*A009940(n-2)) fi: end; seq(A009940(n), n=0..20); with(orthopoly):seq(n!*L(n, 1), n=0..20); (C. Ronaldo)
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MATHEMATICA
| (NestList[ #-Integrate[ #, x ]&, 1, 32 ]/.x:>1) Range[ 0, 32 ]!
Table[ n! LaguerreL[ n, 1 ], {n, 18} ]
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CROSSREFS
| Row sums of A021009.
Sequence in context: A047018 A064813 A183932 * A081163 A082133 A060111
Adjacent sequences: A009937 A009938 A009939 * A009941 A009942 A009943
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KEYWORD
| sign
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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