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Search: id:A135351
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| A135351 |
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a(n) = (2^n+3-7*(-1)^n+3*0^n)/6; or a(0) = 0 and for n > 0, a(n) = A005578(n-1)-(-1)^n. |
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5
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| 0, 2, 0, 3, 2, 7, 10, 23, 42, 87, 170, 343, 682, 1367, 2730, 5463, 10922, 21847, 43690, 87383, 174762, 349527, 699050, 1398103, 2796202, 5592407, 11184810, 22369623, 44739242, 89478487, 178956970
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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seq(sum(binomial(n,k)*f[k]/k!,k=0..n),n=1..30)= =2, 4, 9, 22, 57, 154, 429, 1222, 3537, 10354,... = A099754
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FORMULA
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G.f.: G(x)= x*(1/(1-2*x)+2/(1-x)+1)/2/(1+x) E.g.f: E(x)=(exp(2*x)+3*exp(x)-7*exp(-x)+3)/6
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MAPLE
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G(x):=x*(1/(1-2*x)+2/(1-x)+1)/2/(1+x): f[0]:=G(x): for n from 1 to 30 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n]/n!, n=0..30);
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PROGRAM
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(MAGMA) a135351:=func< n | (2^n+3-7*(-1)^n+3*0^n)/6 >; [ a135351(n): n in [0..32] ]; [From Klaus Brockhaus, Dec 05 2009]
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CROSSREFS
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Cf. A005578, A099754.
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KEYWORD
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easy,nonn,new
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Dec 07 2007
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EXTENSIONS
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First part of definition corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 05 2009
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