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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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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| 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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PROG
| (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
| Cf. A005578, A099754.
Sequence in context: A021496 A151929 A007492 * A079451 A049799 A087985
Adjacent sequences: A135348 A135349 A135350 * A135352 A135353 A135354
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KEYWORD
| easy,nonn
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AUTHOR
| Miklos Kristof (kristmikl(AT)freemail.hu), Dec 07 2007
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EXTENSIONS
| First part of definition corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 05 2009
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