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A126156
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Column 0 and row sums of symmetric triangle A126155.
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6
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1, 1, 7, 139, 5473, 357721, 34988647, 4784061619, 871335013633, 203906055033841, 59618325600871687, 21297483077038703899, 9127322584507530151393, 4621897483978366951337161, 2730069675607609356178641127
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..14.
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FORMULA
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a(n) = sum(k=0..n, A087736(n,k)*3^(n-k) ). - Philippe DELEHAM, Jul 17 2007
It appears that sum(n>=0, a(n)*x^(2*n)/(2*n)! ) = sqrt( sec(sqrt(2)*x) ).
G.f.: 1/(1-x/(1-6x/(1-15x/(1-28x/(1-45x/(1-66x/(1-91x/(1-... or
1/U(0), U(k)=1-x(k+1)(2k+1)/U(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 31 2011
G.f.: 1/U(0) where U(k)= 1 - (4*k+1)*(4*k+2)*x/(2 - (4*k+3)*(4*k+4)*x/U(k+1)) ; (continued fraction, 2-step). - Sergei N. Gladkovskii, Oct 24 2012
G.f.: 1/G(0) where G(k) = 1 - x*(k+1)*(2*k+1)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jan 11 2013.
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MAPLE
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A126156 := proc(n)
sqrt(sec(sqrt(2)*z)) ;
coeftayl(%, z=0, 2*n) ;
%*(2*n)! ;
end;
seq(A126156(n), n=0..10) ; # Sergei N. Gladkovskii, Oct 31 2011
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CROSSREFS
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Cf. A126155; diagonals: A126157, A126158.
Sequence in context: A137463 A221375 A190195 * A082162 A085708 A054606
Adjacent sequences: A126153 A126154 A126155 * A126157 A126158 A126159
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Dec 20 2006
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STATUS
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approved
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