A124394 Inverse of Fine number renewal array.

1, 0, 1, -1, 0, 1, -2, -2, 0, 1, -3, -4, -3, 0, 1, -4, -5, -6, -4, 0, 1, -5, -4, -6, -8, -5, 0, 1, -6, 0, 0, -6, -10, -6, 0, 1, -7, 8, 14, 8, -5, -12, -7, 0, 1, -8, 21, 36, 36, 20, -3, -14, -8, 0, 1, -9, 40, 63, 72, 65, 36, 0, -16, -9, 0, 1

Offset

0,7

Comments

Inverse of A065600. Row sums are A057681(n+1). Diagonal sums are A124395.

Links

Table of n, a(n) for n=0..65.

Formula

Riordan array ((1-2x)/(1-x)^2,x(1-2x)/(1-x)^2); Number triangle T(n,k)=sum{j=0..k+1, C(k+1,j)C(n-j+k+1,2k+1)(-2)^j};

Example

Triangle begins
1,
0, 1,
-1, 0, 1,
-2, -2, 0, 1,
-3, -4, -3, 0, 1,
-4, -5, -6, -4, 0, 1,
-5, -4, -6, -8, -5, 0, 1,
-6, 0, 0, -6, -10, -6, 0, 1

Crossrefs

Sequence in context: A374395 A220074 A059259 * A086460 A321884 A136431

Adjacent sequences: A124391 A124392 A124393 * A124395 A124396 A124397

Keyword

easy,sign,tabl

Author

Paul Barry, Oct 30 2006

Status

approved