A229660 - OEIS

%I #8 Jan 26 2014 17:12:21

%S 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,-9,0,0,0,0,0,0,0,1,-8,36,0,0,0,

%T 0,0,0,1,-7,28,-84,0,0,0,0,0,1,-6,21,-56,126,0,0,0,0,1,-5,15,-35,70,

%U -126,0,0,0,1,-4,10,-20,35,-56,84,0,0,1,-3,6,-10

%N 10-section a(10n+k) gives k-th differences of a for k=0..9 with a(n)=0 for n<9 and a(9)=1.

%H Alois P. Heinz, <a href="/A229660/b229660.txt">Table of n, a(n) for n = 0..10000</a>

%F a(10*n+k) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=0..9.

%p a:= proc(n) option remember; local m, q;

%p       m:= irem(n, 10, 'q'); `if`(n<10, `if`(n=9, 1, 0),

%p       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m))

%p     end:

%p seq(a(n), n=0..100);

%Y Cf. A005590, A229653, A229654, A229655, A229656, A229657, A229658, A229659.

%K sign,look,eigen

%O 0,20

%A _Alois P. Heinz_, Sep 27 2013