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A130103
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Expansion of e.g.f. e^(2x)-(1+x)*e^x+x.
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10
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0, 1, 1, 4, 11, 26, 57, 120, 247, 502, 1013, 2036, 4083, 8178, 16369, 32752, 65519, 131054, 262125, 524268, 1048555, 2097130, 4194281, 8388584, 16777191, 33554406, 67108837, 134217700, 268435427, 536870882, 1073741793, 2147483616
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OFFSET
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0,4
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COMMENTS
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Essentially the same as the Euler numbers A000295.
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LINKS
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FORMULA
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G.f.: x(1-3x+5x^2-2x^3)/((1-x)^2*(1-2x)).
E.g.f.: e^(2x)-(1+x)*e^x+x.
a(n) = 2^n-n-1+C(1,n)-C(0,n).
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EXAMPLE
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G.f. = x + x^2 + 4*x^3 + 11*x^4 + 26*x^5 + 57*x^6 + 120*x^7 + 247*x^8 + ...
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+n od: seq(a[n], n=0..30); # Zerinvary Lajos, Feb 22 2008
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MATHEMATICA
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Join[{0, 1}, LinearRecurrence[{4, -5, 2}, {1, 4, 11}, 40]] (* Harvey P. Dale, May 16 2014 *)
a[ n_] := If[ n < 2, Boole[n == 1], 2^n - (1 + n)]; (* Michael Somos, Aug 17 2015 *)
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PROG
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(PARI) {a(n) = if( n<2, n==1, 2^n - (1+n))}; /* Michael Somos, Aug 17 2015 */
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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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STATUS
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approved
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