A113291 a(n) = A113290(n,1)/(n+1) for n>=0, where A113290 is the matrix log of triangle A113287.

0, 0, 0, 1, -2, 4, -7, 13, -24, 48, -99, 221, -512, 1268, -3247, 8773, -24400, 70896, -211347, 653541, -2068472, 6755684, -22541135, 77305981, -270435640, 969413776, -3539893923, 13212871629, -50180362320, 194412817844, -765590169935, 3070433223317

Offset: 0

Author

Paul D. Hanna, Oct 23 2005

Keywords

• sign

Crossrefs

Cf. A113287, A113288, A113290, A072374.

Programs

PARI

a(n)=if(n<3,0,(-1)^(n-3)*sum(k=0,n-3,sum(j=0,k\2,(k-j)!/(k-2*j)!)))

Formula

G.f. satisfies: A(x) = x^3*((2+x)/(1+x) + (1+x)*A'(x))/(2+3*x+2*x^2). a(n+3) = (-1)^n*Sum_{k=0..n} Sum{j=0..[k/2]} (k-j)!/(k-2*j)! for n>=0. a(n+3) = -a(n+2) + (-1)^n*A072374(n) for n>=1.