A051256 Numbers formed from binomial coefficients (mod 2) interpreted as digits in factorial base.

1, 3, 7, 33, 121, 843, 5167, 46233, 362881, 3991683, 40279687, 522910113, 6227383801, 93409304523, 1313941673647, 22324392524313, 355687428096001, 6758061133824003, 122000787836928007, 2561305169719296033

Offset: 0

Author

Antti Karttunen, Oct 24 1999

Keywords

• nonn
• nice
• base

Examples

			a(5) = 1! + 2! + 5! + 6! = 843 (only the first, second, fifth and sixth terms are odd in row 5 of Pascal's Triangle).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..448

Crossrefs

Cf. A001317, A001339, A048757, A047999.

Programs

Maple

A051256(n) := proc(n) local i; RETURN(add(((binomial(n,i) mod 2)*((i+1)!)),i=0..n)); end;

Mathematica

Table[Sum[(k+1)!Mod[Binomial[n,k],2],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Feb 14 2013 *)

Python

from math import factorial
def A051256(n):
    return sum(0 if ~n & k else factorial(k+1) for k in range(n+1)) # Chai Wah Wu, Feb 08 2016

Formula

a(n) = Sum_{k=0..n} (k+1)!(C(n, k) mod 2).