A091699 Row sums of triangle A091698.

1, 0, -1, 3, -9, 30, -109, 420, -1685, 6960, -29391, 126291, -550359, 2426502, -10803801, 48507843, -219377949, 998436792, -4569488371, 21016589073, -97090411019, 450314942682, -2096122733211, 9788916220518

Offset: 0

Author

Christian G. Bower, Jan 29 2004

Keywords

• sign

Comments

Hankel transform is (-1)^n. - Paul Barry, Jun 17 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A091698.

Programs

Mathematica

CoefficientList[Series[2/(3+3*x-Sqrt[1+6*x+5*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 12 2014 *)

PARI

a(n)=polcoeff(2/(3+3*x-sqrt(1+6*x+5*x^2+x*O(x^n))),n,x) \\ Paul D. Hanna

Formula

G.f.: A(x) = 2/(3+3*x - sqrt(1+6*x+5*x^2)). - Paul D. Hanna, Feb 23 2004

Conjecture: 2*n*a(n) + (13*n-16)*a(n-1) + 4*(4*n-7)*a(n-2) + 5*(n-2)*a(n-3) = 0. - R. J. Mathar, Nov 24 2012

a(n) ~ (-1)^(n+1) * 5^(n+3/2) / (72 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 12 2014