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

0,20

Links

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

Formula

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

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);

Crossrefs

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

Sequence in context: A193581 A270034 A228635 * A306757 A340982 A334624

Adjacent sequences: A229657 A229658 A229659 * A229661 A229662 A229663

Keyword

sign,look,eigen

Author

Alois P. Heinz, Sep 27 2013

Status

approved