OFFSET
1,5
LINKS
Indranil Ghosh, Rows 1..100, flattened
FORMULA
G.f.: -(x*sqrt(4*x+1)*y+x*y)/(x*sqrt(4*x+1)*y+x*y-2).
Sum_{n>=m) T(n,m)*x^n is expansion of (x*(1+sqrt(1+4*x))/2)^m.
EXAMPLE
Triangle begins
1;
1, 1;
-1, 2, 1;
2, -1, 3, 1;
-5, 2, 0, 4, 1;
14, -5, 1, 2, 5, 1;
-42, 14, -3, 0, 5, 6, 1;
MATHEMATICA
Flatten[Table[If[n==m, 1, (-1)^(n-m-1)*m*Binomial[2n-3m-1, n-m-1]/(n-m)], {n, 1, 11}, {m, 1, n}]] (* Indranil Ghosh, Feb 28 2017 *)
PROG
(Maxima)
taylor(1/(1-y*A(x))-1, x, 0, 10, y, 0, 10);
(PARI) a(n, m)=if(n==m, 1, (-1)^(n-m-1)*m*binomial(2*n-3*m-1, n-m-1)/(n-m));
tabl(nn)=for(n=1, nn, for(m=1, n, print1(a(n, m), ", ")); print)
tabl(11); \\ Indranil Ghosh, Feb 28 2017
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Vladimir Kruchinin, Apr 14 2016
STATUS
approved