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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = Sum (k+1)!(C(n, k) mod (2+k)), k=0..n

Example

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

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 *)

Crossrefs

Cf. A001317, A001339, A048757, A047999, A051256.

Sequence in context: A231497 A309473 A349058 * A135482 A360475 A126614

Adjacent sequences: A051254 A051255 A051256 * A051258 A051259 A051260

Keyword

nonn,nice,base

Author

Antti Karttunen, Oct 24 1999

Status

approved