1,1

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."

a(n) = Prod[i=i..n] p(i+1)^T(n,i), where T(n,i), are Cataln's triangle as in a009766.

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.

Cf. A007188, A007318, A009766.

Sequence in context: A069261 A053608 A123261 this_sequence A007189 A114628 A135424

Adjacent sequences: A124058 A124059 A124060 this_sequence A124062 A124063 A124064

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 03 2006