OFFSET
0,3
COMMENTS
FORMULA
G.f.: Sum_{n>=0, k>=0} T(n, k)*y^k*x^n = A(x)*A(xy)/(1-y) where A(x) is g.f. of A002212.
T(0, k)=T(1, 0)=1. T(n+1, 0)=T(n, 0)+T(n, n), n>0. T(n, k)=T(n, k-1)+T(k, 0)T(n-k, 0), k>0. T(n, k)=T(n, n), k>n.
EXAMPLE
T(5,3)=T(5,2)+T(3,0)T(5-2,0)=203+10*3=233.
{1}, {1,2}, {3,4,7}, {10,13,16,26}, {36,46,55,65,101},...
PROG
(PARI) T(n, k)=if(k<0 || n<0, 0, if(n==0, 1, if(k==0, T(n-1, 0)+if(n>1, T(n-1, n-1)), T(n, k-1)+T(k, 0)*T(n-k, 0))))
CROSSREFS
KEYWORD
AUTHOR
Paul D. Hanna, Jul 18 2002
STATUS
approved