A367568 a(n) = Product_{k=0..n} (4*k)! / k!^4.

1, 24, 60480, 22353408000, 1409672968704000000, 16539333509029163728896000000, 38185078618454141182825889242546176000000, 18043150250179542387558306410182977707728856678400000000, 1796395750154420920494206475343190362781863323574704301041254400000000000

Offset

0,2

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = Product_{k=0..n} binomial(4*k,k) * binomial(3*k,k) * binomial(2*k,k).

a(n) = A268505(n) / A000178(n)^4.

a(n) = A268505(n) / A168488(n).

a(n) = A007685(n) * A268196(n) * A262261(n).

a(n) ~ A^(15/4) * sqrt(Gamma(1/4)) * 2^(4*n^2 + 7*n/2 - 7/6) * exp(3*n/2 - 5/16) / (n^(3*n/2 + 17/16) * Pi^(3*n/2 + 7/4)), where A is the Glaisher-Kinkelin constant A074962.

Mathematica

Table[Product[(4*k)!/k!^4, {k, 0, n}], {n, 0, 10}]
Table[Product[Binomial[4*k, k] * Binomial[3*k, k] * Binomial[2*k, k], {k, 0, n}], {n, 0, 10}]

Crossrefs

Cf. A000178, A008977, A268505, A168488, A268196, A262261.

Cf. A007685, A367567, A367569, A367570, A367571.

Sequence in context: A158664 A125048 A003920 * A052504 A159388 A172628

Adjacent sequences: A367565 A367566 A367567 * A367569 A367570 A367571

Keyword

nonn

Author

Vaclav Kotesovec, Nov 23 2023

Status

approved