OFFSET
0,5
FORMULA
T(n, k) = Sum {a_1, a_2, ...a_n with a_1+2*a_2+...+n*a_n=k, C(n, a_1)*C(n-1, a_2)*...*C(1, a_n)} .
Sum_{k, k>=0} T(n, k) = 2^(n*(n+1)/2), see A006125.
EXAMPLE
Row n=0 : 1
Row n=1 : 1, 1
Row n=2 : 1, 2, 2, 2, 1
Row n=3 : 1, 3, 5, 8, 10, 10, 10, 8, 5, 3, 1
Row n=4 : 1, 4, 9, 18, 31, 46, 64, 82, 96, 106, 110, 106, 96, 82, 64, 46, 31, 18, 9, 4, 1
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Philippe Deléham, Jan 06 2004, Oct 16 2008
STATUS
approved