A324566 a(n) = Product_{i=0..n, j=0..n} (binomial(2*i, i) + binomial(2*j, j)).

2, 72, 2709504, 15637972132823040, 2676716427588188879089135779840000, 2844659827809077182003221596452154340416256794895644098560000

Offset

0,1

Links

Table of n, a(n) for n=0..5.

Formula

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

d = 1.7552437670085151253596298317411616254914764275962173772854884197280838467...

alfa = 0.0720289309157636194865104906223497131817905230497828189113545663815669...

c = 1.3392511999007422713775779654793976642559410116533455108049762435308676715...

Mathematica

Table[Product[Binomial[2*i, i] + Binomial[2*j, j], {i, 0, n}, {j, 0, n}], {n, 0, 7}]

Crossrefs

Cf. A000984, A007685, A324565, A324567.

Sequence in context: A367492 A221709 A036899 * A276518 A297410 A041647

Adjacent sequences: A324563 A324564 A324565 * A324567 A324568 A324569

Keyword

nonn

Author

Vaclav Kotesovec, Mar 07 2019

Status

approved