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Numbers formed from binomial coefficients (mod 2) interpreted as digits in factorial base.
3

%I #18 Apr 02 2017 01:28:12

%S 1,3,7,33,121,843,5167,46233,362881,3991683,40279687,522910113,

%T 6227383801,93409304523,1313941673647,22324392524313,355687428096001,

%U 6758061133824003,122000787836928007,2561305169719296033

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

%H Chai Wah Wu, <a href="/A051256/b051256.txt">Table of n, a(n) for n = 0..448</a>

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

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

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

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

%o (Python)

%o from math import factorial

%o def A051256(n):

%o return sum(0 if ~n & k else factorial(k+1) for k in range(n+1)) # _Chai Wah Wu_, Feb 08 2016

%Y Cf. A001317, A001339, A048757, A047999.

%K nonn,nice,base

%O 0,2

%A _Antti Karttunen_, Oct 24 1999