A317980 a(n) = Product_{i=1..n} floor(5*i/2).

2, 10, 70, 700, 8400, 126000, 2142000, 42840000, 942480000, 23562000000, 636174000000, 19085220000000, 610727040000000, 21375446400000000, 790891516800000000, 31635660672000000000, 1328697748224000000000, 59791398670080000000000, 2810195737493760000000000

Offset: 1

Author

Vaclav Kotesovec, Oct 02 2018

Keywords

• nonn

Comments

If p > 2 and p is odd, then Product_{i=1..n} floor(p*i/2) ~ (p/2)^n * n! * 2^(1/(2*p)) * sqrt(Pi) / (Gamma(1/2 - 1/(2*p)) * n^(1/(2*p))).

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..390

Crossrefs

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

Programs

Mathematica

Table[Product[Floor[i*5/2], {i, 1, n}], {n, 1, 20}]
RecurrenceTable[{4 a[n] - 10 a[n - 1] - 5 (n - 1) (5 n - 6) a[n - 2] == 0, a[1] == 2, a[2] == 10}, a, {n, 1, 20}] (* Bruno Berselli, Oct 03 2018 *)
FoldList[Times,Floor[5*Range[20]/2]] (* Harvey P. Dale, Sep 17 2020 *)

Formula

a(n) ~ (5/2)^n * n! * 2^(1/10) * sqrt(Pi) / (Gamma(2/5) * n^(1/10)).

Recurrence: 4*a(n) - 10*a(n-1) - 5*(n - 1)*(5*n - 6)*a(n-2) = 0, with n >= 3. - Bruno Berselli, Oct 03 2018