A201050 C(n#, (n-1)#), where n# is the primorial A034386(n), the product of primes <= n.

1, 2, 15, 1, 593775, 1, 1985871372366807082113118777430351536, 1, 1, 1

Offset

1,2

Comments

Next term a(11) has 305 digits.

a(n) = 1 if and only if n is nonprime. When n is composite, n# and (n-1)# are the same, and since C(n, n) = 1, a(n) = 1 as well.

Links

Table of n, a(n) for n=1..10.

Formula

a(n) = binomial(n#, (n-1)#).

a(n) = n^A010051(n)*binomial(n# - 1, (n-1)# - 1). - Arkadiusz Wesolowski, Oct 21 2013

Example

a(3) = 15 because the 3rd primorial is 6, the (3-1)th primorial is 2, and C(6, 2) = 15.
a(5) = (product_{i=5#-3#+1..5#} a(i))/(3#)! = 25*26*27*28*29*30/6! = 593775.

Mathematica

lst = {}; Do[AppendTo[lst, Binomial[Product[Prime[i], {i, n}], Product[Prime[i], {i, n - 1}]]]; AppendTo[lst, Table[1, {Prime[n + 1] - Prime[n] - 1}]], {n, 6}]; Prepend[Flatten[lst], 1]

Prog

(PARI) a(n)=my(k=prod(i=1, primepi(n), prime(i))); binomial(k, k/n) \\ Charles R Greathouse IV, Nov 30 2011

Crossrefs

Cf. A034386.

Sequence in context: A027739 A193307 A331511 * A299321 A357097 A248537

Adjacent sequences: A201047 A201048 A201049 * A201051 A201052 A201053

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 26 2011

Status

approved