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A126156 Column 0 and row sums of symmetric triangle A126155. 6
1, 1, 7, 139, 5473, 357721, 34988647, 4784061619, 871335013633, 203906055033841, 59618325600871687, 21297483077038703899, 9127322584507530151393, 4621897483978366951337161, 2730069675607609356178641127 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = sum(k=0..n, A087736(n,k)*3^(n-k) ). - Philippe Deléham, 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.

G.f.: Q(0), where Q(k) = 1 - x*(2*k+1)*(k+1)/( x*(2*k+1)*(k+1) - 1/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Oct 09 2013

MAPLE

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

MATHEMATICA

a[n_] := SeriesCoefficient[ Sqrt[ Sec[ Sqrt[2]*x]], {x, 0, 2 n}]*(2*n)!; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Nov 29 2013, after Sergei N. Gladkovskii *)

CROSSREFS

Cf. A126155; diagonals: A126157, A126158.

Sequence in context: A137463 A221375 A190195 * A082162 A238692 A085708

Adjacent sequences:  A126153 A126154 A126155 * A126157 A126158 A126159

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 20 2006

STATUS

approved

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Last modified April 16 12:16 EDT 2014. Contains 240591 sequences.