A124061 Multiplicative encoding of Catalan's triangle: Product p(i+1)^T(n,i).

2, 6, 450, 2836181250, 81492043057751910481759423160156250, 4561157026363824997482074305569280581505536351717093893927260661169357729871499327113563125890139588096951624677718591308593750

Offset: 1

Author

Jonathan Vos Post, Nov 03 2006

Keywords

• easy
• nonn

Comments

This is to A009766 "Catalan's triangle T(n,k) (read by rows)" as A007188 "Multiplicative encoding of Pascal triangle: Product p(i+1)^C(n,i)" is to A007318 "Pascal's triangle read by rows."

Examples

			a(1) = p(1)^T(1,1) = 2^1 = 2.
a(2) = p(1)^T(2,1) * p(2)^T(2,2) = 2^1 * 3^1 = 6.
a(3) = p(1)^T(3,1) * p(2)^T(3,2) * p(3)^T(3,3) = 2^1 * 3^2 * 5^2 = 450.
a(4) = 2^1 * 3^3 * 5^5 * 7^5 = 2836181250.
a(5) = 2^1 * 3^4 * 5^9 * 7^14 * 11^14 = 81492043057751910481759423160156250.
a(6) = 2^1 * 3^5 * 5^14 * 7^28 * 11^42 * 13^42.
		

Crossrefs

Cf. A007188, A007318, A009766.

Formula

a(n) = Prod[i=i..n] p(i+1)^T(n,i), where T(n,i) are Catalan's triangle as in A009766.