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

%I A051256 #18 Apr 02 2017 01:28:12
%S A051256 1,3,7,33,121,843,5167,46233,362881,3991683,40279687,522910113,
%T A051256 6227383801,93409304523,1313941673647,22324392524313,355687428096001,
%U A051256 6758061133824003,122000787836928007,2561305169719296033
%N A051256 Numbers formed from binomial coefficients (mod 2) interpreted as digits in factorial base.
%H A051256 Chai Wah Wu, <a href="/A051256/b051256.txt">Table of n, a(n) for n = 0..448</a>
%F A051256 a(n) = Sum_{k=0..n} (k+1)!(C(n, k) mod 2).
%e A051256 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 A051256(n) := proc(n) local i; RETURN(add(((binomial(n,i) mod 2)*((i+1)!)),i=0..n)); end;
%t A051256 Table[Sum[(k+1)!Mod[Binomial[n,k],2],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Feb 14 2013 *)
%o A051256 (Python)
%o A051256 from math import factorial
%o A051256 def A051256(n):
%o A051256     return sum(0 if ~n & k else factorial(k+1) for k in range(n+1)) # _Chai Wah Wu_, Feb 08 2016
%Y A051256 Cf. A001317, A001339, A048757, A047999.
%K A051256 nonn,nice,base
%O A051256 0,2
%A A051256 _Antti Karttunen_, Oct 24 1999