A229660 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.

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

Offset: 0

Author

Alois P. Heinz, Sep 27 2013

Keywords

• sign
• look
• eigen

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

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

Programs

Maple

a:= proc(n) option remember; local m, q;
      m:= irem(n, 10, 'q'); `if`(n<10, `if`(n=9, 1, 0),
      add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m))
    end:
seq(a(n), n=0..100);

Formula

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