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A054116
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T(n,n-1), array T as in A054115.
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5
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1, 2, 8, 32, 152, 872, 5912, 46232, 409112, 4037912, 43954712, 522956312, 6749977112, 93928268312, 1401602636312, 22324392524312, 378011820620312, 6780385526348312, 128425485935180312, 2561327494111820312
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OFFSET
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1,2
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COMMENTS
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For n>1, equals (-1)^(n+1) * BarnesG(n+2) times the determinant of the n X n matrix whose (i,j)-entry equals (i!-1)/i! if i=j and equals 1 otherwise. - John M. Campbell, Sep 14 2011
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LINKS
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FORMULA
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Let u(1)=1, u(2)=0 and u(k)=u(k-1)-1/k*u(k-2) then for n>2 a(n-1)=-u(n)*n!. - Benoit Cloitre, Nov 05 2004
Conjecture: a(n) - (n+1)*a(n-1) + n*a(n-2) = 0. - R. J. Mathar, Jun 13 2013
G.f.: 1 - 1/(1-x) + W(0)/(1-x), where W(k) = 1 - x*(k+2)/( x*(k+2) - 1/(1 - x*(k+1)/( x*(k+1) - 1/W(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Aug 25 2013
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MAPLE
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a[1]:=1; a[2]:=2; for n from 3 to 20 do a[n]:=a[n-1]+factorial(n) end do; # Francesco Daddi, Aug 03 2011
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MATHEMATICA
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PROG
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(PARI) u1=1; u2=0; z=-1; for(n=3, 100, u3=u2+z/n*u1; u1=u2; u2=u3; if(n>0, print1(-(u3)*n!, ", "))) \\ Benoit Cloitre
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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