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A124061 Multiplicative encoding of Catalan's triangle: Product p(i+1)^T(n,i). 2
2, 6, 450, 2836181250, 81492043057751910481759423160156250, 4561157026363824997482074305569280581505536351717093893927260661169357729871499327113563125890139588096951624677718591308593750 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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."

LINKS

Table of n, a(n) for n=1..6.

FORMULA

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

EXAMPLE

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.

Sequence in context: A053608 A199239 A123261 * A007189 A114628 A135424

Adjacent sequences:  A124058 A124059 A124060 * A124062 A124063 A124064

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 03 2006

STATUS

approved

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Last modified September 19 18:47 EDT 2018. Contains 315210 sequences. (Running on oeis4.)