A319949 a(n) = Product_{i=1..n} floor(4*i/3).

1, 2, 8, 40, 240, 1920, 17280, 172800, 2073600, 26956800, 377395200, 6038323200, 102651494400, 1847726899200, 36954537984000, 776045297664000, 17072996548608000, 409751917166592000, 10243797929164800000, 266338746158284800000

Offset: 1

Author

Vaclav Kotesovec, Oct 02 2018

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..429

Crossrefs

Cf. A004773, A010786, A180736, A275062, A319948, A319950.

Programs

Mathematica

Table[Product[Floor[i*4/3], {i, 1, n}], {n, 1, 20}]
RecurrenceTable[{27*(3*n - 7)*a[n] == 54*(2*n - 5)*a[n-1] + 12*(12*n^2 - 42*n + 35)*a[n-2] + 8*(n-2)*(2*n - 5)*(3*n - 4)*(4*n - 9)*a[n-3], a[1]==1, a[2]==2, a[3]==8}, a, {n, 1, 20}]
FoldList[Times,Floor[4 Range[20]/3]] (* Harvey P. Dale, Mar 21 2024 *)

PARI

a(n) = prod(i=1, n, (4*i)\3); \\ Michel Marcus, Oct 03 2018

Formula

a(n) ~ (4/3)^n * n! * 2*sqrt(Pi) / (3^(1/4) * Gamma(1/4) * n^(1/4)).

Recurrence: 27*(3*n - 7)*a(n) = 54*(2*n - 5)*a(n-1) + 12*(12*n^2 - 42*n + 35)*a(n-2) + 8*(n-2)*(2*n - 5)*(3*n - 4)*(4*n - 9)*a(n-3).