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 A106539 a(1)=1, a(2)=1, a(n) = (n-1)*a(n-1) - (n-2)*a(n-2) - ... - a(1) for n>=3. 1
 1, 1, 1, 0, -6, -36, -192, -1104, -7248, -54816, -472512, -4573824, -49064448, -577130496, -7381281792, -101940854784, -1511556077568, -23945902043136, -403579232182272, -7209532170092544, -136064164749017088, -2705030337674674176, -56501002847058788352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Beginning with a(0)=0, a(1)=1 gives 0, 1, 2, 4, 8, 16, ..., 2^(n-1). LINKS G. C. Greubel, Table of n, a(n) for n = 1..400 FORMULA D-finite with recurrence: a(n) = n*a(n-1) - 2*(n-2)*a(n-2), a(1)=1, a(2)=1. - Georg Fischer, Jun 18 2021 a(n) = e^(-2)*( - Gamma(n)*E_{n}(-2) + 2^(n-1)*(-Ei(2) + e^2 - Pi*i), where Ei(x) and E_{n}(x) are exponential integrals. - G. C. Greubel, Sep 03 2021 EXAMPLE a(7) = 6*(-36) - 5(-6) - 4*0 - 3*1 - 2*1 - 1*1 = -216 + 30 - 0 - 3 - 2 - 1 = -192. MAPLE nmax:=24; a[1]:=1: a[2]:=1: for n from 3 to nmax do a[n]:=(n-1)*a[n-1]-add(k*a[k], k=1..n-2) od: seq(a[n], n=1..nmax); # Emeric Deutsch, Feb 03 2006 MATHEMATICA RecurrenceTable[{a[n]==n*a[n-1] - 2*(n-2)*a[n-2], a[1]==a[2]==1}, a[n], {n, 1, 20}] (* Georg Fischer, Jun 18 2021 *) PROG (MAGMA) [n le 2 select 1 else n*Self(n-1) - 2*(n-2)*Self(n-2): n in [1..30]]; // G. C. Greubel, Sep 03 2021 (Sage) def a(n): return 1 if (n<3) else n*a(n-1) - 2*(n-2)*a(n-2) [a(n) for n in (1..30)] # G. C. Greubel, Sep 03 2021 CROSSREFS Cf. A001571. Sequence in context: A209904 A146883 A159721 * A215453 A267229 A048980 Adjacent sequences:  A106536 A106537 A106538 * A106540 A106541 A106542 KEYWORD easy,sign AUTHOR Alexandre Wajnberg, May 08 2005 EXTENSIONS More terms from Emeric Deutsch, Feb 03 2006 Definition adapted to offset by Georg Fischer, Jun 18 2021 STATUS approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)