A085457 Sum_{i=0..n} Sum_{j=0..i} a(j) * a(i-j) = (-11)^n.

1, -6, 48, -438, 4206, -41586, 418980, -4277130, 44089320, -457891170, 4783741248, -50218890738, 529300238574, -5597562756894, 59366869030668, -631200956847558, 6725615443683870, -71800018913609970, 767806202604650880, -8223081959016322530, 88187484604146004506

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Jul 01 2003

Keywords

• easy
• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..960

Crossrefs

Cf. A085455, A085456.

Programs

Mathematica

CoefficientList[Series[Sqrt[(1-x)/(1+11 x)], {x, 0, 20}], x]

PARI

a(n) = sum(k=0, n, (-3)^k*binomial(n-1, n-k)*binomial(2*k, k)); \\ Seiichi Manyama, Feb 03 2023

Formula

G.f.: A(x)=Sqrt((1-x)/(1+11x)).

From Seiichi Manyama, Feb 03 2023: (Start)

a(n) = Sum_{k=0..n} (-3)^k * binomial(n-1,n-k) * binomial(2*k,k).

n*a(n) = -2*(5*n-2)*a(n-1) + 11*(n-2)*a(n-2). (End)