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A144866 Shadow transform of C(n+4,5) = A000389(n+4).

%I A144866 #13 Sep 16 2019 15:47:30
%S A144866 1,1,2,1,1,3,5,2,4,1,5,3,5,8,1,2,5,6,5,1,11,7,5,6,1,7,4,8,5,4,5,2,11,
%T A144866 8,4,7,5,7,11,2,5,15,5,9,4,8,5,6,5,1,12,8,5,6,3,13,12,7,5,4,5,8,22,2,
%U A144866 8,16,5,11,11,6,5,12,5,7,1,8,25,16,5,2,4,8,5,22,5,7,11,15,5,6,25,8,11,8,5,5
%N A144866 Shadow transform of C(n+4,5) = A000389(n+4).
%H A144866 Alois P. Heinz, <a href="/A144866/b144866.txt">Table of n, a(n) for n = 1..10000</a>
%H A144866 Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. (<a href="http://math.berkeley.edu/~halbeis/publications/psf/seq.ps">ps</a>, <a href="http://math.berkeley.edu/~halbeis/publications/pdf/seq.pdf">pdf</a>); see Definition 7 for the shadow transform.
%H A144866 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%p A144866 shadow:= proc(p) proc(n) local j;
%p A144866            add(`if`(modp(p(j), n)=0, 1, 0), j=0..n-1) end
%p A144866          end:
%p A144866 f:= proc(k) proc(n) binomial (n+k-1,k) end end:
%p A144866 a:= n-> shadow(f(5))(n):
%p A144866 seq(a(n), n=1..120);
%Y A144866 5th column of A144871. Cf. A007318.
%K A144866 nonn
%O A144866 1,3
%A A144866 _Alois P. Heinz_, Sep 23 2008