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A123166 Row sums of A123162. 2
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; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

FORMULA

a(n) = 1 + Sum_{k=0..n} binomial(2n-1, 2k-1). - Paul Barry, May 26 2008

a(n) = A052539(n-2), n > 1. - R. J. Mathar, Jun 18 2008

From Sergei N. Gladkovskii, Dec 20 2011: (Start)

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). (End)

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, Mar 20 2008

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}]

CROSSREFS

Sequence in context: A090902 A150012 A150013 * A052539 A008932 A167809

Adjacent sequences:  A123163 A123164 A123165 * A123167 A123168 A123169

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Oct 02 2006

EXTENSIONS

Edited by N. J. A. Sloane, Oct 04 2006

STATUS

approved

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Last modified February 28 08:43 EST 2020. Contains 332323 sequences. (Running on oeis4.)