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Search: id:A130103
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| A130103 |
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Expansion of e^(2x)-(1+x)*e^x+x. |
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+0
2
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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
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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a(n)=A130102(n+1)/2. Partial sums are A130104. Essentially the same as the Euler numbers A000295.
a(n)=sum_{i=1..n} i*2^(n-i) - Ctibor O. ZIZKA (ctibor.zizka(AT)seznam.cz), Feb 23 2008
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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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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 (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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CROSSREFS
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Cf. A000295.
Sequence in context: A030196 A000295 A125128 this_sequence A034334 A036891 A014630
Adjacent sequences: A130100 A130101 A130102 this_sequence A130104 A130105 A130106
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 07 2007
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