OFFSET
0,9
LINKS
Alex Fink, Richard K. Guy, and Mark Krusemeyer, Partitions with parts occurring at most thrice, Contributions to Discrete Mathematics, Vol 3, No 2 (2008), pp. 76-114.
FORMULA
Recurrence: T(n, k) = T(n-1, k)-T(n-1, k-1)-T(n-2, k); T(n, k)=0 for n<0, k>n, k<0; T(n, n)=(-1)^n; T(n, n-1)=(-1)^n*(1-n).
G.f.: (1-x)/(1+(y-1)*x+x^2). [Vladeta Jovovic, Dec 14 2009]
From Peter Bala, Jul 13 2021: (Start)
Riordan array ( (1 - x)/(1 - x + x^2), -x/(1 - x + x^2) ).
EXAMPLE
Triangle begins:
1;
0, -1;
-1, -1, 1;
-1, 1, 2, -1;
0, 3, 0, -3, 1;
...
MAPLE
A098493 := proc (n, k)
add((-1)^(k+binomial(n-j+1, 2))*binomial(floor((1/2)*n+(1/2)*j), j)* binomial(j, k), j = k..n);
end proc:
seq(seq(A098493(n, k), k = 0..n), n = 0..10); # Peter Bala, Jul 13 2021
PROG
(PARI) T(n, k)=if(k>n||k<0||n<0, 0, if(k>=n-1, (-1)^n*if(k==n, 1, -k), if(n==1, 0, if(k==0, T(n-1, 0)-T(n-2, 0), T(n-1, k)-T(n-2, k)-T(n-1, k-1)))))
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Ralf Stephan, Sep 12 2004
STATUS
approved