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%I #13 May 01 2014 02:49:07
%S 1,3,11,43,231,1337,9739,76209,706109,6914977,78150249,920172983,
%T 12216376453,168531536319,2571960399839,40581616143967,
%U 701349512411763,12460393480873445,240094506439569631,4749510978132662277
%N Numbers formed from binomial coefficients (mod 2+k) interpreted as digits in factorial base.
%H Vincenzo Librandi, <a href="/A051257/b051257.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Sum (k+1)!(C(n, k) mod (2+k)), k=0..n
%e a(5) = (1 mod 2)1!+(5 mod 3)2!+(10 mod 4)3!+(10 mod 5)4!+(5 mod 6)5!+(1 mod 7)6! = 1*1+2*2+2*6+0*24+5*120+1*720 = 1337
%p a(n) := proc(n) local i; RETURN(add(((binomial(n,i)mod(i+2))*((i+1)!)),i=0..n)); end;
%t a[n_] := Sum[(k+1)!*Mod[Binomial[n, k], 2+k], {k, 0, n}]; Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Sep 09 2013 *)
%Y Cf. A001317, A001339, A048757, A047999, A051256.
%K nonn,nice,base
%O 0,2
%A _Antti Karttunen_, Oct 24 1999
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