A051257 Numbers formed from binomial coefficients (mod 2+k) interpreted as digits in factorial base.
1, 3, 11, 43, 231, 1337, 9739, 76209, 706109, 6914977, 78150249, 920172983, 12216376453, 168531536319, 2571960399839, 40581616143967, 701349512411763, 12460393480873445, 240094506439569631, 4749510978132662277
Offset: 0
Examples
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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
-
Maple
a(n) := proc(n) local i; RETURN(add(((binomial(n,i)mod(i+2))*((i+1)!)),i=0..n)); end;
-
Mathematica
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 *)
Formula
a(n) = Sum (k+1)!(C(n, k) mod (2+k)), k=0..n