A324565 a(n) = Product_{i=0..n, j=0..n} (C(i)+C(j)), where C(k) = Catalan(k) = A000108(k).

2, 16, 5184, 3292047360, 431257150704844800000, 1660988174371634812975670031600844800000, 29842277901990912803108442836098281105491323166448779304684748800000

Offset

0,1

Links

Table of n, a(n) for n=0..6.

Formula

a(n) ~ c * d^n * 2^(4*n^3/3 + 3*n^2) * exp(3*n^2/4) / (Pi^(n^2/2) * n^(3*n^2/2 + 3*n - alfa)), where

d = 1.755243767008515125359629831741161625491476427596217377285488419728083846...

alfa = 0.033913207252709141540468528132950860454628430850651543265936300855299...

c = 1.31959917222402005903928675604752142566298009509...

Mathematica

Table[Product[CatalanNumber[i] + CatalanNumber[j], {i, 0, n}, {j, 0, n}], {n, 0, 7}]

Crossrefs

Cf. A000108, A003046, A324566.

Sequence in context: A088321 A061301 A180962 * A306729 A325049 A334912

Adjacent sequences: A324562 A324563 A324564 * A324566 A324567 A324568

Keyword

nonn

Author

Vaclav Kotesovec, Mar 07 2019

Status

approved