OFFSET
0,4
COMMENTS
FORMULA
G.f.: 2/(1+y+(1-y)*sqrt(1+4*x-4*x^2)).
T(n,m) = (-1)^(n-m)*(2*m+1)*Sum_{k=0..n} C(k,n-k)*C(2*k,k-m)/(m+k+1). - Vladimir Kruchinin, Apr 18 2015
EXAMPLE
Rows begin:
[1],
[ -1,1],
[3,-4,1],
[ -9,15,-7,1],
[31,-58,36,-10,1],
[ -113,229,-170,66,-13,1],
[431,-924,775,-372,105,-16,1],
[ -1697,3795,-3481,1939,-691,153,-19,1],
[6847,-15822,15542,-9674,4072,-1154,210,-22,1],...
Matrix inverse equals triangle A101275:
[1],
[1,1],
[1,4,1],
[1,13,7,1],
[1,44,34,10,1],...
PROG
(PARI) {T(n, k)=polcoeff(polcoeff(2/(2*y+(1-y)*(1+sqrt(1+4*x-4*x^2+x*O(x^n)))), n)+y*O(y^k), k)}
(Maxima)
T(n, m):=(-1)^(n-m)*(2*m+1)*(sum((binomial(k, n-k)*binomial(2*k, k-m))/(m+k+1), k, 0, n)); /* Vladimir Kruchinin, Apr 18 2015 */
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Dec 27 2004
STATUS
approved