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A103137
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First column of inverse of Delannoy triangle.
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5
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1, -1, 2, -6, 22, -90, 394, -1806, 8558, -41586, 206098, -1037718, 5293446, -27297738, 142078746, -745387038, 3937603038, -20927156706, 111818026018, -600318853926, 3236724317174, -17518619320890, 95149655201962, -518431875418926, 2832923350929742, -15521467648875090
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OFFSET
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0,3
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COMMENTS
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First column of A103136. The positive sequence has g.f. 1+xS(x). It is the first column of the inverse of the signed Delannoy triangle which has general term T(n,k)=if(k<=n, sum{j=0..k, 2^j*C(n-k,j)C(k,j)}(-1)^(n-k),0).
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LINKS
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FORMULA
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G.f.: 1-xS(-x), where S(x) is the g.f. of the large Schroeder numbers A006318.
Conjecture: n*a(n) +3*(2*n-3)*a(n-1) +(n-3)*a(n-2)=0. - R. J. Mathar, Nov 26 2012
a(n) ~ (-1)^n * sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^n / (2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Feb 13 2014
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MATHEMATICA
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CoefficientList[Series[1+x*(1+x-(1+6*x+x^2)^(1/2))/(2*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 13 2014 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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