A324567 a(n) = Product_{i=0..n, j=0..n} (binomial(2*i, j) + binomial(2*j, i)).

2, 8, 2400, 1247616000, 47391629172572160000, 5433273487668074503912921497600000000, 84476763043100284572577776893541858819157327099409203200000000

Offset

0,1

Links

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

Formula

a(n) ~ c * d^n * exp(2*n^3/3 + 9*n^2/4) / (2^(n^2) * Pi^(n^2/2) * n^(n^2/2 + 5*n/6 - alfa)), where

d = 2.631186542501652610455988727776308850706336468478433795517960445788077147...

alfa = 0.094637735750903047180156176044316953484876143616883847755312100285099...

c = 0.121223472988717836553569221604723373713338356783096...

Mathematica

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

Crossrefs

Cf. A000984, A007685, A324566, A324568.

Sequence in context: A027733 A054874 A174736 * A135238 A133376 A179056

Adjacent sequences: A324564 A324565 A324566 * A324568 A324569 A324570

Keyword

nonn

Author

Vaclav Kotesovec, Mar 07 2019

Status

approved