A085455 Sum_{i=0..n} Sum_{j=0..i} a(j) * a(i-j) = (-3)^n.

1, -2, 4, -10, 26, -70, 192, -534, 1500, -4246, 12092, -34606, 99442, -286730, 829168, -2403834, 6984234, -20331558, 59287740, -173149662, 506376222, -1482730098, 4346486256, -12754363650, 37461564504, -110125172682, 323990062452, -953883382354, 2810310510110, -8284915984726

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: A(x)=Sqrt((1-x)/(1+3x)).

G.f.: G(0), where G(k)= 1 + 4*x*(4*k+1)/( (x-1)*(4*k+2) - x*(x-1)*(4*k+2)*(4*k+3)/(x*(4*k+3) + (x-1)*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 26 2013

From Seiichi Manyama, Feb 03 2023: (Start)

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

n*a(n) = -2*n*a(n-1) + 3*(n-2)*a(n-2). (End)

Mathematica

CoefficientList[Series[Sqrt[(1-x)/(1+3x)], {x, 0, 30}], x]

Prog

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

Crossrefs

Absolute values are in A025565.

Sequence in context: A084575 A081881 A025565 * A055226 A097085 A071962

Adjacent sequences: A085452 A085453 A085454 * A085456 A085457 A085458

Keyword

easy,sign

Author

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

Status

approved