A048804 Triangle: T(n,k)=b(n)/(b(k)*b(n-k)) where b is A048803.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 3, 2, 1, 1, 5, 5, 5, 5, 1, 1, 6, 15, 10, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 2, 7, 14, 35, 14, 7, 2, 1, 1, 3, 3, 7, 21, 21, 7, 3, 3, 1, 1, 10, 15, 10, 35, 42, 35, 10, 15, 10, 1, 1, 11, 55, 55, 55, 77, 77, 55, 55, 55, 11, 1, 1, 6, 33, 110, 165, 66

Offset: 0

Author

Christian G. Bower, Apr 15 1999

Keywords

• nonn
• tabl

Examples

			1;
1,1;
1,2,1;
1,3,3,1;
1,2,3,2,1;
1,5,5,5,5,1;
where the last batch arises from 60/(1*60), 60/(1*12), 60/(2*6), 60/(6*2), 60/(12*1), 60/(60*1).
		

Links

• Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.

Programs

Maple

A048804 := proc(n,k)
    A048803(n)/A048803(k)/A048803(n-k) ;
end proc:
seq(seq(A048804(n,k),k=0..n),n=0..20) ; # R. J. Mathar, Mar 02 2025