A176266 Binomial(prime(n),s)/prime(n) where s is the sum of the decimal digits of n.

1, 1, 2, 5, 42, 132, 1144, 3978, 35530, 1, 15, 210, 2470, 22386, 228459, 2908360, 37584261, 284291205, 3701413144, 35, 852, 19019, 349812, 6529292, 132435472, 2000945100, 24366118700, 328386663605, 3520256293710, 2072, 81375, 2271776, 59988852, 1227434238, 33401522154, 584134601050, 11919696387170, 234924043375476, 3924875235562164, 208335

Offset: 1

Author

Michel Lagneau, Dec 07 2010

Keywords

• nonn
• base

Comments

For n = 10^p, a(n) = 1.

Examples

			a(5) = 42 because prime(5) = 11, s = 5,  binomial(11,5)/11 = 462/11=42.
a(16)=2908360 because prime(16)=53, s=7, binomial(53,7)/53 =154143080/53 = 2908360.
		

Crossrefs

Cf. A075872.

Programs

Maple

A176266 := proc(n) binomial(ithprime(n),A007953(n))/ithprime(n) ; end proc:
seq(A176266(n),n=1..20) ;

Mathematica

Table[Binomial[Prime[n],Total[IntegerDigits[n]]]/Prime[n],{n,40}] (* Harvey P. Dale, Oct 25 2020 *)

Sage

A176266 = lambda n: binomial(nth_prime(n), sum(n.digits()))/nth_prime(n) # D. S. McNeil, Dec 08 2010

Formula

a(n) = A007318( A000040(n), A007953(n))/A000040(n).

a(n) = A060604(n)/A000040(n), n<10.