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1, 2, 5, 17, 65, 257, 1025, 4097, 16385, 65537, 262145, 1048577, 4194305, 16777217, 67108865, 268435457, 1073741825, 4294967297, 17179869185, 68719476737, 274877906945
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n)=1+sum{k=0..n, C(2n-1,2k-1)}; - Paul Barry (pbarry(AT)wit.ie), May 26 2008
a(n)=A052539(n-2), n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2008
G.f.: (1 - 3*x - x^2)/(x-1)/(4*x-1) ;
E.g.f.: exp(4*x)/4+exp(x)-1/4 = (G(0)-1)/4 ; G(k) =1 + 4/(4^k-x*16^k/(x*4^k+(k+1)/G(k+1))) ; (continued fraction). - Sergei N. Gladkovskii, Dec 20 2011
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MAPLE
| a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=4*a[n-1] od: seq(a[n]+sum((k), k=0..1), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
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MATHEMATICA
| t[n_, m_] = If [n == m == 0 || m == 0, 1, (2*n - 1)!/((2*(n - m))!*(2*m - 1)!)]; a = Table[Sum[t[n, m], {m, 0, n}], {n, 0, 20}]
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CROSSREFS
| Sequence in context: A090902 A150012 A150013 * A052539 A008932 A167809
Adjacent sequences: A123163 A123164 A123165 * A123167 A123168 A123169
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KEYWORD
| nonn
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 02 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 04 2006
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