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A144869 Shadow transform of C(n+7,8) = A000581(n+7).

%I A144869 #11 Sep 16 2019 18:07:27
%S A144869 1,1,2,1,3,1,1,1,6,2,8,1,8,1,8,1,8,6,8,1,3,6,8,1,6,7,6,1,8,7,8,1,21,
%T A144869 14,4,7,8,8,21,1,8,2,8,8,21,7,8,1,2,6,21,4,8,5,26,1,21,7,8,6,8,13,11,
%U A144869 1,28,21,8,11,21,10,8,6,8,5,16,4,11,21,8,1,6,8,8,2,26,6,21,7,8,20,12,7,21,13
%N A144869 Shadow transform of C(n+7,8) = A000581(n+7).
%H A144869 Alois P. Heinz, <a href="/A144869/b144869.txt">Table of n, a(n) for n = 1..1000</a>
%H A144869 Lorenz Halbeisen and Norbert Hungerbuehler, <a href="https://www.semanticscholar.org/paper/Number-theoretic-aspects-of-a-combinatorial-Halbeisen-Hungerb%C3%BChler/5743ff2f9c14d22d1a9e570d6951a7c9ef79a612">Number theoretic aspects of a combinatorial function</a>, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform.
%H A144869 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%p A144869 shadow:= proc(p) proc(n) local j; add (`if` (modp(p(j), n)=0, 1,0), j=0..n-1) end end: f:= proc(k) proc(n) binomial (n+k-1,k) end end: a:= n-> shadow (f(8))(n): seq (a(n), n=1..100);
%Y A144869 8th column of A144871. Cf. A007318.
%K A144869 nonn
%O A144869 1,3
%A A144869 _Alois P. Heinz_, Sep 23 2008