A126124 Triangle, matrix inverse of A124733, companion to A123965.
1, -2, 1, 5, -5, 1, -13, 19, -8, 1, 34, -65, 42, -11, 1, -89, 210, -183, 74, -14, 1, 233, -654, 717, -394, 115, -17, 1, -610, 1985, -2622, 1825, -725, 165, -20, 1, 1597, -5911, 9134, -7703, 3885, -1203, 224, -23, 1
Offset: 1
Examples
First few rows of the triangle are:
1;
-2, 1;
5, -5, 1;
-13, 19, -8, 1;
34, -65, 42, -11, 1;
-89, 210, -183, 74, -14, 1;
...
Triangle (n >= 0 and 0 <= k <= n) [0,-2,-1/2,-1/2,0,0,0,0,0,...] DELTA [1,0,1/2,-1/2,0,0,0,0,0,...] begins:
1;
0, 1;
0, -2, 1;
0, 5, -5, 1;
0, -13, 19, -8, 1;
0, 34, -65, 42, -11, 1;
0, -89, 210, -183, 74, -14, 1;
0, 233, -654, 717, -394, 115, -17, 1;
Formula
Sum_{k=1..n} (-1)^(n-k)*T(n,k) = A001835(n). - Philippe Deléham, Jul 14 2007
T(n,k) = T(n-1,k-1) - 3*T(n-1,k) - T(n-2,k). - Philippe Deléham, Dec 13 2011
T(n,k) = (-1)^(n+k)*Sum_{m=k..n} binomial(m,k)*binomial(m+n,2*m). - Wadim Zudilin, Jan 11 2012
G.f.: (1+x)*x*y/(1+3*x+x^2-x*y). - R. J. Mathar, Aug 11 2015
Extensions
Corrected by Philippe Deléham, Jul 14 2007
More terms from Philippe Deléham, Dec 13 2011
Comments